Catheter systems and related methods for mapping, minimizing, and treating cardiac fibrillation

ABSTRACT

Catheters, systems, and related methods for optimized for mapping, minimizing, and treating cardiac fibrillation in a patient, including an array of at least one stacked electrode pair, each electrode pair including a first electrode and a second electrode, wherein each electrode pair is configured to be orthogonal to a surface of a cardiac tissue substrate, wherein each first electrode is in contact with the surface to record a first signal, and wherein each second electrode is separated from the first electrode by a distance which enables the second electrode to record a second signal, wherein the catheter is configured to obtain one or more measurements from at least a first signal and a second signal in response to electrical activity in the cardiac tissue substrate indicative of a number of electrical circuit cores and distribution of the electrical circuit cores for a duration across the cardiac tissue substrate.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/844,753, filed Mar. 15, 2013, which claims priority to andincorporates by reference the entire contents of provisional applicationNo. 61/753,387, filed on Jan. 16, 2013.

TECHNICAL FIELD

The present disclosure relates generally to methods and systems fordetecting and treating cardiac fibrillation. More specifically, thepresent disclosure relates to physiologic, particularlyelectrophysiologic, methods and systems for preventing, treating, and atleast minimizing if not terminating cardiac fibrillation by mappingcardiac fibrillation and optimizing the placement of ablation lesions.

BACKGROUND OF THE INVENTION

Atrial fibrillation, which accounts for almost one-third of alladmissions to a hospital for a cardiac rhythm disturbance, is anuncontrolled twitching or quivering of muscle fibers (fibrils) resultingin an irregular and often rapid heart arrhythmia associated withincreased mortality and risk of stroke and heart failure. See, e.g.,Calkins et al., Treatment of Atrial Fibrillation with Anti-arrhythmicDrugs or Radio Frequency Ablation: Two Systematic Literature Reviews andMeta-analyses, 2(4) Circ. Arrhythmia Electrophysiol. 349-61 (2009).Atrial fibrillation may be paroxysmal or chronic, and the causes ofatrial fibrillation episodes are varied and often unclear; however,atrial fibrillation manifests as a loss of electrical coordination inthe top chambers of the heart. When fibrillation occurs in the lowerchambers of the heart, it is called ventricular fibrillation. Duringventricular fibrillation, blood is not pumped from the heart, and suddencardiac death may result.

Existing treatments for cardiac fibrillation include medications andother interventions to try to restore and maintain normal organizedelectrical activity to the atria. When medications, which are effectiveonly in a certain percentage of patients, fail to maintain normalelectrical activity, clinicians may resort to incisions made during openheart surgery or minimally-invasive ablation procedures, whereby linesof non-conducting tissue are created across the cardiac tissue in anattempt to limit the patterns of electrical excitation to include onlyorganized activity and not fibrillation. Id. at 355. If sufficient andwell-placed, the non-conducting tissue (e.g., scar tissue) willinterfere with and normalize the erratic electrical activity, ideallyrendering the atria or ventricles incapable of supporting cardiacfibrillation.

Catheter ablation targeting isolation of the pulmonary veins has evolvedover the past decade and has become the treatment of choice fordrug-resistant paroxysmal atrial fibrillation. The use of ablation fortreatment of persistent atrial fibrillation has been expanding, withmore centers now offering the procedure.

Unfortunately, the success of current ablation techniques for treatingcardiac fibrillation is less than desirable, for example, curing onlyabout 70% of atrial fibrillation patients. Id. at 354. In contrast,ablation for treating heart arrhythmias other than fibrillation issuccessful in more than 95% of patients. Spector et al., Meta-Analysisof Ablation of Atrial Flutter and Supraventricular Tachycardia, 104(5)Am. J. Cardiol. 671, 674 (2009). One reason for this discrepancy insuccess rates is due to the complexity of identifying the ever-changingand self-perpetuating electrical activities occurring during cardiacfibrillation. Without the ability to accurately determine the sourcelocations and mechanisms underlying cardiac fibrillation in anindividual patient and develop a customized ablation strategy,clinicians must apply generalized strategies developed on the basis ofcardiac fibrillation pathophysiologic principles identified in basicresearch and clinical studies from other patients. The goal of ablationis to alter atrial and/or ventricular physiology and, particularly,electrophysiology such that the chamber no longer supports fibrillation;it is insufficient to simply terminate a single episode. However,ablation lesions have the potential to cause additional harm to thepatient (e.g., complications including steam pops and cardiacperforation, thrombus formation, pulmonary vein stenosis, andatrio-esophageal fistula) and to increase the patient's likelihood ofdeveloping abnormal heart rhythms (by introducing new abnormalelectrical circuits that lead to further episodes of fibrillation).

In addition, existing catheters with their associated electrodeconfigurations that are used to assist in preventing, treating, and atleast minimizing if not terminating cardiac fibrillation have severalshortcomings, including that the electrodes are too large, theinter-electrode spacing is too great, and the electrode configurationsare not suitably orthogonal to the tissue surface. These catheters ofthe prior art tend to prompt time consuming methods since the catheter,and thus its electrodes, have to be moved to a relatively large numberof locations in the heart cavity to acquire sufficient data.Additionally, moving the catheter to different locations so that thecatheter's electrode(s) touch the endocardium is a cumbersome processthat is technically challenging.

Further complicating the use of prior art contact-based catheters is theoccurrence of unstable arrhythmia conditions. Particularly, ventriculartachyarrhythmias may compromise the heart's ability to circulate bloodeffectively. As a result, the patient cannot be maintained in fasttachyarrhythmia's for more than a few minutes, which significantlycomplicates the ability to acquire data during the arrhythmia. Inaddition, some arrhythmias are transient or nonperiodic in nature;therefore, contact-based catheters of the prior art are less suitablefor mapping these arrhythmia's since the sequential contact-basedmethodology is predicated on the assumption that recorded signals areperiodic in nature.

Thus, cardiac fibrillation patients would benefit from new methods andsystems for the preventing, treating, and at least minimizing if notterminating cardiac fibrillation in the underlying “substrate” (i.e.,the tissue on which abnormal electrical circuits of reentry are formed)responsible for the initiation and perpetuation of cardiac fibrillation.These methods and systems would help clinicians minimize or preventfurther episodes and increase the success rate of non-invasive ablationtreatments in cardiac fibrillation patients. There remains a need forpatient-specific, map-guided ablation strategies that would minimize thetotal amount of ablation required to achieve the desired clinicalbenefit by identifying ablation targets and optimizing the mostefficient means of eliminating the targets.

SUMMARY OF THE INVENTION

The methods and systems of the present invention are predicated on therecognition and modeling of the actual physiologic and, particularly,electrophysiologic principles underlying fibrillation. For instance, theprior ablation art fails to recognize the importance of and providemethods and systems for gauging a patient's fibrillogenicity, e.g., howconducive the atria are to supporting atrial fibrillation and how muchablation is required for successful treatment, detecting and mappingfibrillation, optimizing the distribution of ablation lesions for botheffectiveness and efficiency, and guiding ablation based on quantitativefeedback methods and systems. These methods and systems of theembodiments of the present invention are directed, therefore, todefining successful strategies, procedures, and clinical outcomes thatare tailored for each patient with cardiac fibrillation.

In an embodiment, catheter optimized for mapping cardiac fibrillation ina patient, including an array of at least one stacked electrode pair,each electrode pair including a first electrode and a second electrode,wherein each electrode pair is configured to be orthogonal to a surfaceof a cardiac tissue substrate, wherein each first electrode is incontact with the surface to record a first signal, and wherein eachsecond electrode is separated from the first electrode by a distancewhich enables the second electrode to record a second signal, whereinthe catheter is configured to obtain one or more measurements from atleast a first signal and a second signal in response to electricalactivity in the cardiac tissue substrate indicative of a number ofelectrical circuit cores and distribution of the electrical circuitcores for a duration across the cardiac tissue substrate in thepatient's heart.

In another embodiment, catheter optimized for assessing efficacy of anablation procedure in a patient, comprising: an array of at least onestacked electrode pair, each electrode pair including a first electrodeand a second electrode, wherein each electrode pair is configured to beorthogonal to a surface of a cardiac tissue substrate, wherein eachfirst electrode is in contact with the surface to record a first signal,and wherein each second electrode is separated from the first electrodeby a distance which enables the second electrode to record a secondsignal, wherein the catheter is configured to obtain one or moremeasurements from at least a first signal and a second signal inresponse to electrical activity in the cardiac tissue substrateindicative of a number of electrical circuit cores and distribution ofthe electrical circuit cores for a duration across the cardiac tissuesubstrate in the patient's heart.

The details of one or more embodiments of the present invention are setforth in the accompanying drawings and the description below. Otherfeatures, objects, and advantages of the present invention will beapparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C illustrate the relationship between the source-sink ratioand wave curvature according to some embodiments of the presentinvention;

FIGS. 2A-2B illustrate reentry circuits using a topological perspectiveof the tissue substrate, in accordance with embodiments of the presentinvention;

FIGS. 3A-3B illustrate how the minimum path of a curling wavefront islimited by tissue excitation wavelength, in accordance with embodimentsof the present invention;

FIGS. 4A-4F illustrate rotor termination resulting from circuittransection via core collision with a tissue boundary according to someembodiments of the present invention;

FIGS. 5A-5C illustrates the rotor ablation requirement of a linearlesion from the rotor core to the tissue edge, in accordance with someembodiments of the present invention;

FIGS. 6A-6C are simulated patterns of cardiac tissue activity producedby a computational model, in accordance with embodiments of the presentinvention;

FIGS. 7A-7C illustrate surface topology and reentry, in accordance withembodiments of the present invention;

FIG. 8 illustrates the impact of boundary-length-to-surface-area ratioon the duration of multi-wavelet reentry according to some embodimentsof the present invention;

FIGS. 9A-9D illustrate how ablation lines increase theboundary-length-to-surface-area ratio and decrease the duration ofmulti-wavelet reentry, in accordance with embodiments of the presentinvention;

FIGS. 10A-10B illustrate the circuit density maps, particularly FIG. 10Aillustrates homogenous tissue without a short wavelength patch, and FIG.10B illustrates heterogeneous tissue with a wavelength patch, inaccordance with embodiments of the present invention;

FIG. 11 illustrates graphically ablation lesion characteristics andfitness of tissue with homogeneous circuit density, in accordance withembodiments of the present invention;

FIGS. 12A-12B illustrate graphically the relationship of ablationdensity versus circuit density, in accordance with embodiments of thepresent invention;

FIG. 13 is a system component block diagram, in accordance withembodiments of the present invention;

FIG. 14 is a plot of simultaneous measurements of the atrialfibrillatory cycle length from surface ECG/EKG and the left and rightatrial appendages according to some embodiments of the presentinvention;

FIGS. 15A-15D illustrate graphically atrial fibrillation cycle length(AFCL) correlation, particularly, FIG. 15A illustrates relationshipbetween mean sureface ECG/EKG/AFCL a measurement from 10 and 30 CL, FIG.15B illustrates relationship between surgace ECG AFCL from 10 CL andAFCL using time frequency analysis, FIG. 15C illustrates therelationship between surface ECG AFCL from 10 CL and the LAA CL and FIG.15D illustrates the relationship between ECG AFCL from 10 CL and RAA CLin accordance with embodiments of the present invention;

FIGS. 16A-16C are Bland-Altman plots illustrating the relationshipbetween the RAA cycle length and the cycle lengths from time frequencyanalysis and surface ECG/EKG, in accordance with embodiments of thepresent invention;

FIG. 17 is a plot of the receiver-operator characteristic curve for thesurface ECG/EKG cycle length, in accordance with embodiments of thepresent invention;

FIGS. 18A-18B are plots of Kaplan-Meier curve analyses of the incidenceof recurrent arrhythmia following ablation procedure, in accordance withembodiments of the present invention;

FIGS. 19A-19F illustrate temporal, spatial, and spatiotemporal variationof tissue excitation, in accordance with embodiments of the presentinvention;

FIG. 20 illustrates electrode geometry, spacing, and position, inaccordance with embodiments of the present invention;

FIG. 21A is a graph illustrating fractionation as a function of temporalvariation by the number of deflections versus stimulus cycle length, inaccordance with embodiments of the present invention;

FIG. 21B is a series of virtual unipolar electrograms from tissueexcited at decreasing cycle lengths, in accordance with embodiments ofthe present invention;

FIG. 22A is a graph of the number of deflections in unipolar recordingsas a function of spatiotemporal variation and electrode resolution, inaccordance with embodiments of the present invention;

FIG. 22B is a series of virtual unipolar electrograms from tissueexcited with increasing spatiotemporal variation, in accordance withembodiments of the present invention;

FIGS. 23A-23B are fluoroscopic images of a catheter in the coronarysinus, in accordance with embodiments of the present invention;

FIG. 23C is a set of electrograms simultaneously recorded during sinusrhythm and atrial fibrillation with varying inter-electrode spacing, inaccordance with embodiments of the present invention;

FIG. 24 is a schematic of a dipole current source located at ±δ/2 aboutthe origin and a bipolar pair of electrodes of diameter d and height lseparated by Δ and located at height z₀ along the y-axis, in accordancewith embodiments of the present invention;

FIGS. 25A-25B are graphical plots where FIG. 25A illustrates acomparison of predicted potential recorded by a unipolar electrode as afunction of lateral distance from a dipole current source (solid line)and the potential measured experimentally in a saline bath (filledcircles) and FIG. 25B illustrates a corresponding plot for bipolarrecording, in accordance with embodiments of the resent invention;

FIGS. 26A-26B are graphical plots where FIG. 26A illustrates thepotential due to a dipole current source recorded by a unipolarelectrode as a function of lateral distance from the source, showing howresolution is quantified in terms of peak width at half maximum heightand FIG. 26B illustrates the corresponding plot for a bipolar electrode,in accordance with embodiments of the present invention;

FIGS. 27A-27B are graphical plots of simulates bipolar electrograms, inaccordance with embodiments of the present invention;

FIGS. 28A-28C graphically illustrate the resolution of a unipolarelectrode recording of a dipole current source as assessed in terms ofC_(min) and W_(1/2), In accordance with embodiments of the presentinvention;

FIGS. 29A-29D are graphical plots illustrating resolution of a bipolarelectrode recording of a dipole current source, as assessed in terms ofC_(min) and W_(1/2), in accordance with embodiments of the presentinvention;

FIG. 30 is a process flowchart for identifying an optimal spatialresolution for local tissue with spatiotemporal variation, in accordancewith embodiments of the present invention;

FIGS. 31A-31B illustrate a catheter with a contact bipolar electrodeconfiguration, in accordance with embodiments of the present invention;

FIG. 32 illustrates the orientation of electrodes relative to anelectric dipole, in accordance with embodiments of the presentinvention;

FIG. 33 illustrates the orientation of electrodes relative to near andfar field charges, in accordance with embodiments of the presentinvention;

FIG. 34 graphically illustrates near fields spatial electrograms from amodel, in accordance with embodiments of the present invention;

FIG. 35 graphically illustrates far field spatial electrograms from amodel, in accordance with embodiments of the present invention;

FIG. 36 illustrates graphically electrical potential recordings at asingle electrode, in a model, in accordance with embodiments of thepresent invention;

FIG. 37 graphically illustrates membrane voltage underneath a singleelectrode, in a model, in accordance with embodiments of the presentinvention;

FIGS. 38A-38B illustrate a catheter with an orthogonal, close, unipolar(“OCU”) electrode configuration, in accordance with embodiments of thepresent invention;

FIG. 39 illustrates the difference between a first catheter with aninter-electrode axis orthogonal to a tissue surface and a secondcatheter with an inter-electrode axis that is not orthogonal to thetissue surface, in accordance with embodiments of the present invention;

FIG. 40 illustrates an example of improved spatial resolution obtainedby use of an OCU electrode configuration, in accordance with embodimentsof the present invention;

FIGS. 41A-41C illustrates the edge extension and windowing processapplied to an exemplary transformation between the tissue membranecurrent density field and the potential field at height, in accordancewith embodiments of the present invention;

FIGS. 42A-42D illustrate examples of deconvolution, in accordance withembodiments of the present invention;

FIGS. 43A-43L illustrate maps of membrane current density, in accordancewith embodiments of the present invention;

FIGS. 44A-44B illustrate graphically mean square residual for theobserved and deconvolved signals relative to the true signal for the twoactivation pattern shown in FIGS. 43A-43L, in accordance withembodiments of the present invention;

FIGS. 45A-45L illustrate true current density, observed signal, anddeconvolved signal using different array electrodes, in accordance withembodiments of the present invention;

FIGS. 46A-46B graphically illustrate the mean square residual for theobserves and deconvolved signals relative to the true signal for the twoactivation patterns shown in FIGS. 45A-45L, in accordance withembodiments of the present invention;

FIGS. 47A-47I illustrate effects of electrode height on the resolutionof a rotor showing the true current density, the observed signal. andthe deconvolved signal at different heights, in accordance withembodiments of the present invention;

FIGS. 48A-48D graphically illustrate mean square residual for theobserved and deconvolved signals relative to the true signal for theactivation pattern shown in FIGS. 47A-47I;

FIGS. 49 and 50 illustrate two-dimensional multi-electrode arrays, inaccordance with embodiments of the present invention;

FIG. 51A is a process flowchart for improving spatial resolution usingdeconvolution, in accordance with embodiments of the present invention;

FIG. 51B illustrates an exemplary window, in accordance with embodimentsof the present invention;

FIGS. 52A-52B illustrate a catheter with an OCU electrode configurationfor identifying an optimal spatial resolution for local tissue withspatiotemporal variation, in accordance with embodiments of the presentinvention;

FIGS. 53 and 54 illustrate different views of a catheter configured forboth mapping and treating cardiac fibrillation according to someembodiments of the present invention;

FIG. 55 is a process flowchart for assessing fibrillogenicity in apatient according to some embodiments of the present invention;

FIGS. 56A-56C illustrate the relationship between electrogram recordingsand a resulting electrogram frequency map of a tissue substrate, inaccordance with embodiments of the present invention;

FIG. 57 illustrates the impact of selecting a threshold frequency todefine the size and number of high circuit core density regions across atissue substrate, in accordance with embodiments of the presentinvention;

FIG. 58 illustrates a hierarchical tree-like structure provided by agenetic algorithm for optimizing lesion placement, in accordance withembodiments of the present invention;

FIG. 59 is a process flowchart for applying a genetic algorithm foroptimizing lesion placement to a map indicating circuit core density anddistribution, in accordance with embodiments of the present invention;

FIG. 60 is a process flowchart for assessing fibrillogenicity in apatient, in accordance with embodiments of the present invention;

FIG. 61 is a process flowchart for treating cardiac fibrillation in apatient using iterative feedback, in accordance with embodiments of thepresent invention;

FIG. 62 is a system diagram, in accordance with embodiments of thepresent invention;

FIGS. 63A-63B are a computer axial tomography scans of a human heart, inaccordance with embodiments of the present invention;

FIGS. 64-65 are two views of a three-dimensional plot of the time totermination of induced episodes of multi-wavelet reentry as a functionof total ablation length and circuit density overlap according to someaspects of the present invention;

FIGS. 66-67 are two views of a three-dimensional plot of the percentinducibility (z-axis) as a function of total ablation length (x-axis)and circuit density overlap (y-axis) in accordance with some aspects ofthe present invention; and

FIGS. 68, 69A-69B, and 70 illustrate catheter designs of alternativeembodiments in accordance with some embodiments of the presentinvention.

DETAILED DESCRIPTION

Embodiments of the present invention include new methods and systems forpreventing, treating, and at least minimizing if not terminating cardiacfibrillation in the substrate responsible for initiation andperpetuation of fibrillation and for optimized treatments of thatsubstrate, which are predicated on the recognition and modeling of theactual physiological information, including the electrophysiologicprinciples, underlying fibrillation. These methods and systems make itpossible for a clinician to develop and implement patient-specific,tailored fibrillation treatment, minimization, and preventionstrategies. More specifically, embodiments of the present inventionallow a clinician to minimize or prevent further episodes and increasethe success rate of ablation in fibrillation patients by preventing“reentry,” which perpetuates fibrillation as described in greater detailbelow.

The methods and systems embodying the present invention are predicatedon new recognitions that electrophysiological measurements, which willbe discussed in detail, are clinically useful for defining successfulstrategies, procedures, and clinical outcomes that are tailored for eachpatient with cardiac fibrillation.

First, new methods and systems for predicting and mapping the densityand distribution of the cores or centers of the reentrant circuits onthe underlying tissue substrate are disclosed according to someembodiments of the present invention. Second, new methods and systemsfor optimizing (for efficacy and efficiency) the placement of ablationlesions to physically interrupt the circuits are disclosed according tosome embodiments of the present invention. Third, these as well as othermethods and systems for assessing fibrillogenicity to inform the extentof ablation required to reduce fibrillogenicity and prevent or at leastminimize further fibrillation episodes are introduced according to someembodiments of the present invention. Fourth, new methods and systemsfor guiding treatment of fibrillation using quantitative feedback anddetermining when sufficient treatment has been provided are disclosedaccording to some embodiments of the present invention. Also disclosedare new catheter systems and methods for determining patient-specificand location-specific tissue spatiotemporal variations, mapping thedensity and distribution of circuit cores, and/or assessing the efficacyof a treatment procedure.

Although the embodiments of the present invention are described withrespect to atrial fibrillation, the same methods and systems would applyto preventing, treating, and at least minimizing if not terminatingventricular fibrillation by mapping ventricular fibrillation andoptimizing the placement of ablation lesions. Cardiac fibrillation,particularly atrial fibrillation, is a progressive disorder, wherein aheart's electrical properties become increasingly conducive tosupporting fibrillation; hence episodes, once initiated, areprogressively less likely to spontaneously terminate.

The outer wall of the human heart is composed of three layers. The outerlayer is the epicardium, or visceral pericardium because it is also theinner wall of the pericardium. The middle layer is the myocardium, whichis composed of cardiac muscle that contracts. The inner layer is theendocardium, which is in contact with the blood that the heart pumps.The endocardium merges with the endothelium of blood vessels and alsocovers heart valves.

The human heart has four chambers, two superior atria and two inferiorventricles. The pathway of blood through the human heart consists of apulmonary circuit and a systemic circuit. Deoxygenated blood flowsthrough the heart in one direction, entering through the superior venacava into the right atrium. From the right atrium, blood is pumpedthrough the tricuspid valve into the right ventricle before being pumpedthrough the pulmonary valve to the pulmonary arteries into the lungs.Oxygenated blood returns from the lungs through the pulmonary veins tothe left atrium. From the left atrium, blood is pumped through themitral valve into the left ventricle before being pumped through theaortic valve to the aorta.

Cardiac Electrophysiology and Principles of Propagation

The study of clinical electrophysiology is essentially comprised ofexamining how electrical excitation develops and spreads through themillions of cells that constitute the heart. Human cardiac tissueconstitutes a complex non-linear dynamic system. Given the enormousnumber of cells in a human heart, this system is capable of generating astaggeringly large number of possible ways that the heart can behave,that is, potential activation patterns as excitation propagates throughthe tissue. Rhythms vary across a spectrum, from the organized andorderly behavior of sinus rhythm, with large coherent waves traversingacross all cells and then extinguishing, to pathologic behaviors duringwhich activation propagates in continuous loops, perpetually re-excitingthe cardiac tissue (via reentry) in structurally defined circuits likethe complex, dynamic and disorganized behavior of cardiac fibrillation.Despite these myriad possibilities, a basic understanding of theprinciples of propagation may be applied to predict how cardiac tissuewill behave under varied circumstances and in response to variousmanipulations.

Cell Excitation and Impulse Propagation

A cell becomes excited when the voltage of its membrane rises above theactivation threshold of its depolarizing currents (i.e., the sodiumcurrent (INa+) and calcium current (ICa++)). To reach activationthreshold, the net trans-membrane current must be sufficient todischarge the membrane capacitance. The cell membrane separates chargesacross the space between its inner and outer surfaces, resulting in avoltage gradient. The size of the voltage gradient is determined by thenumber of charges and the distance by which they are separated.

The membrane capacity to hold charges on its surface, that is, themembrane capacitance, is determined by the surface area of a cellmembrane and its thickness (i.e., the distance by which it separatescharges). The force required to keep these charges from wandering awayfrom a cell surface is generated by the electrical attraction toopposite charges on the other side of the membrane. The thinner themembrane, the closer the charges are to each other and the larger forcethey can exert to resist wandering off (i.e. the distance across thefaces of a capacitor is inversely proportional to its capacitance).

As capacitance increases, the voltage change that results from theaddition of a single charge to the cell membrane is reduced. An increasein capacitance means more charge is required per millivolt increase inmembrane voltage. Because membrane thickness is the same in all cardiaccells, capacitance varies directly with cell size (i.e., surface area)and inversely with intercellular resistance (i.e., well-connected groupsof cells act much like one large cell). Consequently, larger cells orwell-connected groups of cells are more difficult to excite than smalleror poorly connected groups of cells since more current is required toreach activation threshold.

Cardiac cell membranes can simultaneously accommodate inward and outwardcurrents (via separate ion channels/exchangers/pumps). Membranedepolarization is determined not by inward current alone, but rather bynet inward current. If both inward and outward currents exist, theamount of depolarization (or repolarization) is determined by thebalance of these currents. In their resting state, the majority of openchannels in typical atrial and ventricular cells are potassium (K+)channels. This is why the resting membrane potential is nearly equal tothe “reversal potential” for K+. As current enters a cell (e.g., via gapjunctions from a neighboring cell), its membrane will begin todepolarize. This depolarization reduces the force preventing K+ fromtraveling down its concentration gradient. K+ flows out of the cell oncethis concentration gradient force exceeds the voltage gradientcounter-force so that the outside of the cell is less positive than theinside of the cell. This, in turn, results in membrane repolarization.Therefore, in order for inward current to result in depolarization, themagnitude of the inward current must be greater than the magnitude ofthe outward current that it “unleashes.” This resistance to membranedepolarization associated with outward K+ current is amounts to “voltageclamping” (i.e., keeping voltage fixed). A K+ channel open at rest isthe inward rectifier. Cardiac cells that have a large number of inwardrectifier channels have a resting membrane potential close to the K+reversal potential, and a higher capacitance via thedepolarization-resistant voltage clamping action of its inward rectifierchannels.

Source-Sink Relationships

Propagation refers not simply to cell excitation but specifically toexcitation that results from depolarizing current spreading from onecell to its neighbors. Electrical propagation may be described in termsof a source of depolarizing current and a sink of tissue that is to bedepolarized. A source of current from excited cells flows into a sink ofunexcited cells and provides a current to depolarize the unexcited cellsto activation threshold.

A source is analogous to a bucket filled with electrical current, and asink is analogous to a separate bucket into which the source current is“poured.” When the “level” of source current in the sink bucket reachesa threshold for activation, the sink bucket is excited and fillscompletely with current from its own ion channels. The sink bucketitself then becomes part of the source current. With respect to the sinkbucket, the net depolarizing current is the inward/upward current aslimited by the “leak” current or outward/downward current, which isanalogous to a leak in the bottom of the sink bucket. Using this bucketanalogy, the amount of current poured into the sink, in excess of thatrequired to reach activation threshold, is the safety factor, which isthe amount by which source current may be reduced while maintainingsuccessful propagation.

The increased capacitance of multiple sink cells connected via gapjunctions is analogous to two or more sink buckets connected at theirbases by tubes. The intercellular resistance of the tubes (i.e., gapjunctions) influences the distribution of current poured into the firstsink-bucket. With high intercellular resistance in the tube between afirst and second bucket, the majority of the current poured into thefirst bucket will contribute to raising the voltage level of thatbucket, with only a small trickle of current flowing into the secondbucket. As intercellular resistance is reduced, the rate of voltagechange in the first and second buckets progressively equalizes. Withsufficiently low intercellular resistance, the sink effectively doublesin size (and the amount of depolarization of each membrane is reduced byhalf). Therefore, sink size increases as the intercellular resistancedecreases and the number of electrically connected sink cells increases.

All else being equal, the source-sink ratio is determined by the numberof source cells and the number of sink cells to which they areconnected. If the source amplitude is held constant while sink size isincreased, the source-sink ratio is reduced. For example, when multiplesink cells are connected via gap junctions, source current iseffectively diluted, reducing the source sink ratio. Outward currentscompeting with the source current also increase the sink size. As thesource-sink ratio decreases, the rate of propagation (i.e., conductionvelocity) also decreases because it takes longer for each cell to reachactivation threshold.

In the case of a sufficiently low source-sink ratio (i.e., a source-sinkmismatch), the safety factor may diminish to less than zero, excitationmay fail, and propagation may cease. The physical arrangement of cellsin a tissue influences this balance. For example, a structurallydetermined source-sink mismatch occurs when propagation proceeds from anarrower bundle of fibers to a broader band of tissue. The the narrowerbundle of fibers provides a smaller source than the sink of the broaderband of tissue to which it is connected. In this case the source-sinkratio is asymmetric. However, if propagation proceeds in the oppositedirection (i.e., from the broader band of tissue into the narrowerbundle of fibers), the source is larger than the sink, excitationsucceeds, and propagation continues. Therefore, this tissue structuremay result in a uni-directional conduction block and is a potentialmechanism for concealed accessory pathways, as described further below.

The physical dimensions of wavefront also influence the source-sinkratio. For example, source and sink are not balanced in a curvedwavefront. In a convex wavefront the source is smaller than the sink;therefore, convex wave-fronts conduct current more slowly than flat orconcave wave-fronts. Thus the rate and reliability of excitation isproportional to wavefront curvature: as curvature increases, conductionvelocity decreases until critical threshold resulting in propagationfailure. This is the basis of fibrillation.

FIGS. 1A-1C illustrate the relationship between the source-sink ratioand wave curvature according to some aspects of the current invention.In FIG. 1A, a flat wavefront maintain a balance between source 10 andsink 12, while in FIG. 1B, a convex wavefront have a smaller source 10and a larger sink 12. FIG. 1C illustrates a spiral wavefront with acurved leading edge, in which the curvature is progressively greatertowards the spiral center. As curvature increases, conduction velocitydecreases. Thus, the spiral wavefront in FIG. 1C has less curvature butfaster conduction at location 14 than at location 16, where thewavefront has less curvature but faster conduction than at location 18.At the inner most center or core of the wavefront, the source is toosmall to excite the adjacent sink and, due to the source-sink mismatch,propagation fails, resulting in a core of unexcited and/or unexcitabletissue around which rotation occurs.

Reentry

While several mechanisms may contribute to cardiac fibrillation, by farthe most conspicuous culprit in fibrillation is reentry. The fundamentalcharacteristic of reentry is that ongoing electrical activity resultsfrom continuous propagation, as opposed to repeated de novo focalimpulse formation. The general concept of reentry is straight-forward:waves of activation propagate in a closed loop returning to re-excitethe cells within the reentry circuit. Because of the heart's refractoryproperties, a wave of excitation cannot simply reverse directions;reentry requires separate paths for conduction away from and backtowards each site in the circuit.

The details of circuit formation can be quite varied and in some casesquite complex. In the simplest case, a circuit is structurally definedin that physically separated conduction paths link to form a closed loop(resulting in, e.g., atrial flutter). Circuits can also be composed ofpaths that are separated due to functional cell-cell dissociation (e.g.,rotors, to be described further below). In all cases reentry requires:(1) a closed loop of excitable tissue; (2) a conduction block around thecircuit in one direction with successful conduction in the oppositedirection; and (3) a conduction time around the circuit that is longerthan the refractory period of any component of the circuit.

Topologically, a region of tissue substrate may be described as a finitetwo-dimensional sheet of excitable cells. The edges of the sheet form aboundary, resulting in a bounded plane. If a wave of excitationtraverses the plane, it will extinguish at its edges. However, if adisconnected region of unexcited and/or unexcitable cells within theplane, a closed loop may exist with the potential to support reentryprovided the other criteria for reentry are met. Topologically, thisregion of disconnection is an inner boundary, and the result is aninterrupted, bounded plane regardless of whether the disconnection isdue to physical factors (e.g., scar tissue, no gap junctions, and/or ahole formed by a vessel or valve) or functional factors (e.g.,source-sink mismatch and/or refractory conduction block).

FIGS. 2A-2B illustrate reentry circuits using a topological perspectiveof the tissue substrate in accordance with some aspects of the presentinvention. In FIG. 2A, an uninterrupted, bounded plane of tissuesubstrate cannot support reentry. However, in FIG. 2B, the addition of ainner, disconnected region of unexcited and/or unexcitable cells 20transforms the tissue substrate into an interrupted, bounded plane and apotential circuit for reentry.

One benefit of a topological approach is the generalizability with whichit applies to the full range of possible circuits for reentry. Despite amyriad of potential constituents, all reentrant circuits may be modelledas interrupted, bounded planes. Another benefit of a topologic approachis the unification it confers on all treatments for reentry: circuittransection by any means results in termination. Topologically, allcircuit transections constitute transformation back to an uninterrupted,bounded plane.

Reentry may be prevented in two ways: (1) increasing the tissueexcitation wavelength; and (2) physically interrupting the circuits ofreentry by, for example, introducing an electrical boundary (e.g., scartissue formed following an ablation lesion). The embodiments of thepresent disclosure provides methods and systems for effectively andefficiently preventing reentry by the latter method of physicallyinterrupting the circuits and, consequently, reducing the ability of aheart to perpetuate fibrillation.

A reentrant circuit may be transected physically, as with catheterablation, or functionally, as with antiarrhythmic medications (whichmay, e.g., reduce tissue excitability and/or extend the refractoryperiod). Either way, a circuit transection results when a continuousline of unexcited and/or unexcitable cells is created from a tissue edgeto an inner boundary, and the interrupted, bounded plane is transformedinto an uninterrupted, bounded plane.

FIGS. 3A-3B illustrate circuit transection due to refractoryprolongation. In FIG. 3A, if the trailing edge of refractory tissue 32is extended in the direction of the arrow to meet the leading edge ofexcitation 30, such that the entire leading edge encounters unexcitabletissue (“head meets tail”) then, in FIG. 3B, the propagation ends wherethe unexcitable tissue begins 36 and a line of conduction block 38transects the circuit from inner to outer boundary.

Complex Reentrant Circuits: Rotors and Multi-Wavelet Reentry

The self-perpetuating reentry properties of fibrillation are in part theresult of cyclone-like rotating spiral waves of tissue excitation(“rotors”). A rotor is an example of a functional reentrant circuit thatis created when source-sink relationships at the end of an electricalwave create a core of unexcited and/or unexcitable tissue (i.e., a rotorcore) around which rotation occurs. Activation waves propagate radiallyfrom the rotor core, producing a spiral wave that appears as rotationdue to the radial propagation with progressive phase shift.

Rotors can occur even in homogeneous and fully excitable tissue inwhich, based on the timing and distribution of excitation, groups ofcells in separate phases of refractoriness create separate paths whichlink to form a circuit. The simplest rotors have spatially-fixed cores,whereas more complex rotors have cores that are more diffuse and meanderthroughout the tissue. At the highest end of the spectrum, rotorsencountering spatially-varying levels of refractoriness divide to formdistinct daughter waves, resulting in multi-wavelet reentry.

As described above wave curvature influences source-sink balance. Arotor has a curved leading edge, in which curvature is progressivelygreater towards its spiral center of rotation. As curvature increases,conduction velocity decreases. At the spiral center the curvature islarge enough to reduce the safety factor to less than zero, andpropagation fails due to source-sink mismatch, creating a core ofunexcited and/or unexcitable tissue (i.e., a sink) around which rotationoccurs.

If the wavelength at the inner most part of a rotor is shorter than thepath length around the sink, its unexcited and/or unexcitable core iscircular and/or a point. If the wavelength is longer than the pathlength, then the rotor may move laterally along its own refractory tailuntil it encounters excitable tissue at which point it can turn, thusproducing an elongated core. If conduction velocity around its core isuniform, a rotor will remain fixed in space. Alternatively, ifconduction velocity is greater in one part of rotation than another, thea rotor and its core will meander along the tissue substrate.

If the edge of this spiral wave encounters unexcitable tissue it will“break,” and if the newly created wave-ends begin rotation,“daughter-waves” are formed. In the most complex iterations, reentry maycomprise multiple meandering and dividing spiral waves, some with wavelifespans lasting for less than a single rotation.

Terminating and Preventing Reentrant Rhythms

The mechanism of reentry provides insight into the strategies that willresult in its termination: If reentry requires closed circuits thenprevention, minimization, and/or termination requires transection ofthese circuits. Transection can be achieved in several different ways.In the case of fixed anatomic circuits, the circuit simply be physicallytransected with, for example, a linear ablation lesion.

Another approach to transection is to prolong the tissue activationwavelength by increasing refractory period sufficiently that wavelengthexceeds path-length (i.e., “head meets tail”), and the circuit istransected by a line of functional block. Increasing conduction velocitysufficiently would ultimately have the same effect but is not practicaltherapeutically, in part, because conduction velocity itself isproarrhythmic and antiarrhythmic agents are limited by the degree towhich they decrease conduction velocity.

The antiarrhythmic approach to treating multi-wavelet reentry in atrialfibrillation may include: decreasing excitation (thereby increasing theminimum sustainable curvature, increasing core size, meander and corecollision probability) or increasing action potential duration andthereby wavelength (again increasing the probability of corecollision/annihilation). However, as atrial fibrillation progresses,electrical remodeling of the atria render it progressively moreconducive to perpetuation of reentry such that the antiarrhythmic doserequired to sufficiently prolong action potential duration in the atriacan result in proarrhythmia in the ventricles.

Ablation for Reentrant Rhythms

It is relatively straight forward to see how ablation can be used totransect a spatially fixed circuit but less clear how delivery ofstationary ablation lesions can reliably transect moving functionalcircuits. Circuits are spontaneously transected when their core collideswith the tissue edge (annulus) or with a line of conduction block thatis contiguous with the tissue edge.

FIGS. 4A-4F illustrate rotor termination resulting from circuittransection via core collision with a tissue boundary according to someaspects of the present invention. The rotor core 40 moves closer to thetissue edge with each rotation 1-4, shown in FIGS. 4A-4D respectively.Upon collision of the core 40 with the tissue edge, as shown in FIG. 4E,the circuit is transected and reentry is terminated as shown in FIG. 4F.

Based upon this premise it is not surprising that the probability thatmulti-wavelet reentry will perpetuate is inversely proportional to theprobability of such collisions. As tissue area is increased (whilekeeping tissue boundary fixed), the probability of core/boundarycollision is reduced and perpetuation probability enhanced. If the areaover which waves meander is reduced or the number of waves is increased,the probability that all waves will collide/annihilate is increased.Thus, atrial remodeling promotes fibrillation by decreasing theboundary-length-to-surface-area ratio (chamber dilation (surface area)is greater than annular dilation (boundary length)) and by decreasingwavelength (conduction velocity is decreased and action potentialduration is decreased). The circuit transection/collision-probabilityperspective on atrial fibrillation perpetuation suggests the means toreduce atrial fibrillogenicity (tendency to maintain fibrillation). Theboundary-length-to-surface-area ratio can be increased by adding linearablation lesions. In order to transect a rotor circuit, an ablation linemust extend from the tissue edge to the rotor core. Focal ablation atthe center of a rotor simply converts the functional block at its coreinto structural block; ablation transforms spiral wave reentry intofixed anatomic reentry.

FIGS. 5A-5C illustrates the rotor ablation requirement of a linearlesion from the rotor core to the tissue edge in accordance with someaspects of the present invention. In FIG. 5A, focal ablation 50 at arotor core converts a functional circuit (i.e., spiral wave) into astructural circuit but does not eliminate reentry. FIG. 5B illustrateshow reentry continues if a linear lesion does not extend to the rotorcore 52 (similar to a cavo-tricuspid isthmus ablation line that fails toextend all the way to the Eustachian ridge). In FIG. 5C, an ablationline 54 from the rotor core to the tissue edge transects the reentrycircuit. Instead of circulating around its core the wave end travelsalong the ablation line 54 and ultimately terminates at the tissue edge.

Reentrant electrical rhythms persist by repeatedly looping back tore-excite or activate tissue in a cycle of perpetual propagation ratherthan by periodic de novo impulse formation. Due to its refractoryproperties, cardiac tissue activation cannot simply reverse directions.Instead, reentry rhythms or circuits require separate paths fordeparture from and return to each site, analogous to an electricalcircuit.

The components of these reentrant circuits can vary, the anatomic andphysiologic constituents falling along a continuum from lower to higherspatiotemporal complexity. At the lower end of the spectrum, thecircuits are composed of permanent anatomically-defined structures suchas a region of scar tissue; however, circuit components may also befunctional (i.e., resulting from emergent physiologic changes) andtherefore transient, such as occurs when electrical dissociation betweenadjacent fibers allows formation of separate conduction paths.

FIGS. 6A-6C illustrates these concepts using simulated patterns ofcardiac tissue activity produced by a computational model. The reentrantcircuits illustrated in FIGS. 6A-6C are of increasing complexity. FIG.6A illustrates spiral waves of a simple reentrant circuit around astructural inner-boundary region of non-conducting tissue 60 (i.e., asimple rotor with a spatially-fixed core of, e.g., scar tissue). FIG. 6Billustrates spiral waves of a more complex reentrant circuit 62 that isfree to travel the tissue (i.e., a rotor with a functionally-formedcore). Spiral waves are an example of functional reentrant substratecreated when source-sink relationships at the spiral center create acore of unexcited and/or unexcitable tissue around which rotationoccurs. This can occur even in homogeneous and fully excitable tissue inwhich, based on the timing and distribution of excitation, groups ofcells in separate phases of refractoriness create the separate pathswhich link to form a circuit. The simplest spiral-waves have spatiallyfixed cores as in FIG. 6A, whereas more complex examples have cores thatmeander throughout the tissue as in FIG. 6B. At the most complex end ofthe reentry spectrum, spiral-waves encountering spatially varyingrefractoriness can divide to form distinct daughterwaves, resulting inmulti-wavelet reentry. FIG. 6C illustrates multi-wavelet reentry with,for example, daughterwaves 64, 66, and 68 (i.e., multiple rotorsdividing to form daughter waves).

A rotor terminates when: (1) the rotor core (i.e., the center of thewave's rotation) collides with an electrical boundary in the atria,which physically interrupts the circuit of reentry; or (2) the tissueexcitation wavelength is increased beyond the length of the circuit ofreentry, thus physiologically interrupting the circuit of reentry (i.e.,the circuit “interrupts itself” as the leading edge of tissue excitationcollides with the trailing edge of refractory tissue). FIGS. 3A and 3Billustrate how the minimum path of a rotor is limited by tissueexcitation wavelength in accordance with some aspects of the presentinvention. In FIG. 3A, the leading edge 401 of the tissue excitationwave does not overlap the trailing edge 402 of refractory tissue so thereentrant circuit is not interrupted. However, in FIG. 3B, thewavelength of the tissue excitation wave exceeds the length of thecircuit of reentry: the leading edge 403 of the tissue excitation wavemeets the trailing edge 404 of refractory tissue. When the rotorencounters the unexcitable refractory tissue 404, its path—and itscircuit of reentry—is interrupted. When all circuits of reentry havebeen interrupted, when all rotors have been terminated, the fibrillationepisode itself terminates.

Because reentrant circuits may be defined topologically, the cardiactissue substrate, for example, the left atrium, may be viewed as abounded and interrupted plane, which is capable of forming a reentrantcircuit. In the left atrium, the annulus forms the edge or “outer”boundary of the plane, while the pulmonary veins form holes ordiscontinuities interrupting the plane. A discontinuity is any placewithin the tissue across which current does not flow.

A discontinuity may be structural and/or functional. As a result oftissue refractory properties (or source-sink mismatch), a structurallyuninterrupted plane may nonetheless be capable of forming a reentrantcircuit around a functional inner discontinuity, such as a physiologicconduction block. Thus, a heart may be described based upon its physicaltopology (defined by the geometrical structure of the tissue) and basedupon its functional topology (defined by the physiologically possiblepaths of tissue activation).

Topologically, two surfaces are considered homomorphic (i.e., the same)if one surface can be transformed into the other surface by stretching,but not by cutting or pasting. All bounded surfaces with aninner-discontinuity may be considered homomorphic and functionallyidentical. Likewise, all bounded surfaces with an inner discontinuitymay be considered homomorphic and functionally identical. From thisperspective, a bounded surface with no inner discontinuity and a boundedsurface with a discontinuity that is connected to a boundary (i.e., atissue edge) are the same despite being of different shapes because onesurface can be merely stretched to become the other surface. As a resultof tissue refractory properties a structurally uninterrupted plane maynonetheless be capable of forming a circuit (around aninner-discontinuity to physiological conduction block). One can describea physical topology (defined by the tissue structural geometry) and afunctional topology (defined by the physiologically possible paths ofactivation).

Reentry requires a complete electrical circuit; disruption causespropagation to cease. If its circuit is disrupted, reentry isterminated, whether by prolongation of the tissue excitation wavelengthbeyond the circuit length or by physical interruption. As such,termination of fibrillation requires “breaking” each reentrant circuit.Topologically, this equates to converting a tissue substrate from abounded and interrupted plane (capable of reentry) to a bounded butuninterrupted plane. As discussed above, a bounded but uninterruptedplane is functionally identical to a bounded plane in which theinterruption is connected to the boundary. Thus, by connecting anydiscontinuities in a tissue substrate with a tissue edge, the tissuesubstrate may become functionally identical to a bounded butuninterrupted surface and less or no longer capable of supportingreentry. Thus, by connecting any discontinuities in a tissue substratewith a tissue edge, the tissue substrate may become functionallyidentical to a bounded but interrupted surface and less or no longercapable of supporting reentry.

FIGS. 7A-7C illustrate surface topology and reentry in accordance withsome aspects of the present invention. More specifically, FIG. 7Aillustrates a single wave 70 in an uninterrupted plane 72 with an outerboundary; FIG. 7B illustrates an interrupted place with a disconnectedinner-boundary 74; and FIG. 7C illustrates a plane several time-stepsafter an ablation lesion 76 has connected the inner-boundary (e.g., thewave tip) to the tissue edge, thus eliminating the inner bounary. From atopological perspective, despite their differences in shape, a surfacelike the plane in FIG. 7A with no innerdiscontinuity and a surface likethe plane in FIG. 7C with a discontinuity that is connected to thetissue edge are equivalent. That is, FIGS. 7A and 7C are homomorphic.

As with any reentrant rhythm, termination of multi-wavelet reentryrequires circuit disruption. Unfortunately, the circuits involved inmulti-wavelet reentry are spatially complex and temporally varying, soactually achieving circuit disruption is a pragmatic challenge.Nevertheless, the topologic perspective on reentry provides a conceptualframework for deciding where ablation lesions should be placed so as toyield the greatest likelihood of terminating multi-wavelet reentry. Thegoal of ablation is to reconfigure the tissue's topology (structural andfunctional) into that of an uninterrupted plane.

The simplest situation is presented by a fixed spiral-wave. The leadingedge of excitation in spiral-wave reentry is curved, and curvatureincreases progressively until source-sink relationships at the spiralcentre result in propagation failure. As shown in FIG. 7B, the point ofpropagation failure at the wave tip forms the inner-edge of thespiral-wave around which rotation occurs. As shown in FIG. 7C, circuitdisruption requires a lesion to span from the tissue edge to theinnerdiscontinuity at the wave tip.

The situation becomes more complicated with a meandering spiral-wave, asit is difficult to determine where a fixed lesion can be placed that isguaranteed to transect the reentrant circuit. Movement of thespiral-core provides a means to overcome this pragmatic hurdle; spiralmeander can result in collision of the wave tip with a boundary. Infact, the probability of termination (tip/boundary collision) increasesas the ratio of total boundary length to tissue area increases. Linearablation lesions that are contiguous with the tissue edge can increasethe boundary length area ratio and thereby increase the probability oftermination. Note that such lesions do not change the topology of theatrial tissue; it remains an uninterrupted plane, but with a boundarythat becomes progressively long and tortuous as the number of lesionsincreases. As tissue regions with shorter wavelength are more likely tocontain spiral-waves, linear lesions in these areas are more likely tocross a tip-trajectory and cause spiral-wave termination. The crucialpoint remains, however, that all lesions must be placed such that thetopology of the atrial tissue remains that of an uninterrupted plane.

These topological principles of and mechanisms underlying reentryprovide a conceptual framework for optimizing an ablation lesiondistribution that effectively and efficiently prevents, minimizes,and/or terminates reentry of progressively greater complexity. Usingthis framework, a computational model of cardiac excitation wasdeveloped to generate reentrant rhythms with emergent behavior includingformation of stable and meandering spiral waves as well as multi-waveletreentry. To test the impact of linear ablation (lines of electricallyinert cells) on propagation during multiwavelet reentry, the modelrequired a sufficiently small computational burden such that multiplesimulations of extended periods of excitation could be run in amanageable amount of time.

Cells were arranged in a two-dimensional grid, each cell connected toits four neighbours (up, down, left, and right) via electricallyresistive pathways. Each cell had an intrinsic current trajectory(Im—equivalent to net transmembrane current) that followed a prescribedprofile when the cell became excited. Excitation was elicited eitherwhen the current arriving from the four neighbouring cells accumulatedsufficiently to raise the cell voltage (Vm—equivalent to transmembranevoltage) above a specified threshold or when the cell receivedsufficient external stimulation (pacing). Once excited, a cell remainedrefractory (i.e. non-excitable) until Vm repolarized to the excitationthreshold. The duration of a cell's refractory period was thusdetermined by the duration of its action potential. Following theabsolute refractory period, there was a period of relativerefractoriness during which excitation can occur but with decreasedupstroke velocity. Each cell's intrinsic action potential morphology(voltage vs. time) was modulated by its prior diastolic interval andlowest achieved voltage at the time of its depolarization. Thismodulation conferred restitution upon upstroke velocity and actionpotential duration. Tissue heterogeneity was represented by an actionpotential duration that varies randomly about a set mean, which itselfcould also vary across the tissue.

This computational model did not include all the known biophysicaldetails of individual cardiac cells. Nevertheless, it did incorporatethe key behavioural features of individual cells that are required toreproduce realistic global conduction behaviour. This behaviour includedsource-sink relationships with wave curvature-dependent conductionvelocity and safety factor, and the potential for excitable butunexcited cells to exist at the core of a spiral-wave. The computationalmodel thus combined the computational expediency of cellular automatawith the realism of much more complicated models that include processesat the level of the ion channel.

The voltage matrices from each time-step of the cardiac modelsimulations were saved. Each voltage map was converted into a phase mapby performing a Hilbert transform to generate an orthogonalphase-shifted signal from the original signal at each coordinate of thetissue space-time plot (x, y, t). From the original and phase-shiftedsignals, the phase at each coordinate at each time-step was calculated.

The location of the leading edge of each excitation wave was determinedfor each time-step of the simulation (based on the coordinates at whicheach cell first crossed the threshold for excitation). Phasesingularities were identified, and phase singularity sites wereconsidered to represent a spiral wave tip if (1) all phases surroundedthe singularity in sequence (from −Π to Π) and (2) the phase singularitywas located at the end of a leading edge of activation. Space-time plotsof the phase singularities were created to delineate wave-tiptrajectory. The total number of spiral-wave tips (measured during eachtime-step over the sampling interval) divided by the space-time volumewas defined as the spiral-wave-tip density. Spiral waves were initiatedby rapid pacing from two sites in close proximity with an offset in thetiming of impulse delivery. Spiral waves were spatially stable in thesetting of homogeneous tissue (all cells identical) with a shorterwavelength than circuit length. As action potential duration wasincreased (wavelength circuit length), the spiral waves began tomeander. Multi-wavelet reentry resulted when action potential durationwas randomized across the tissue. A region with higher spiral-wavedensity resulted when a patch of tissue with shorter mean actionpotential duration was created.

Consistent with the topological view of ablation strategies, lesionsplaced at the center of spiral waves simply converted a functionaldiscontinuity into a structural discontinuity, but did not result intermination of reentry. Termination required placement of a lesionspanning from the tissue edge to the wave tip. Even a single excitablecell between the lesion and wave tip was sufficient for spiral-waveperpetuation. However, lesions needed only connect the tissue edge tothe outermost extent of the wave tip-trajectory. Meandering spiral wavesterminated when their wave tips collided with a lesion.

To study the ablation of meandering spiral waves and multi-waveletreentry, cellular action potential duration was randomly varied about amean value (75±25 ms) in a set of simulations to produce a randomspatial distribution of refractoriness. Using this approach, variedpatterns of multi-wavelet reentry were initiated by varying thedistribution of action potential duration. To test the hypothesis thatmobile spiral-waves and multi-wavelet reentry are terminated throughprobabilistic collisions with the tissue boundary, the duration ofmulti-wavelet reentry as a function of theboundary-length-to-surface-area ratio was examined. In rectangularsections of tissue, width and height (and thus boundary length) werevaried while surface area remained fixed. The average duration ofmulti-wavelet reentry increased progressively as theboundary-length-to-surface-area ratio was decreased (average duration2.2±1.7×10³ time-steps at a ratio of 0.26; average duration 4.0±2.1×10⁶time-steps at a ratio of 0.125; simulations at the lowest ratio weretruncated at 5.0×10⁶ time-steps; only 2 of 10 simulations terminatedwithin this time frame).

FIG. 8 illustrates the impact of boundary-length-to-surface-area ratioon the duration multi-wavelet reentry according to some aspects of thepresent invention. Keeping tissue area fixed (at 1,600 mm²) the lengthand height were varied such that boundary-length-to-surface-area ratiodecreased from top to bottom: 0.26, 0.2125, 0.145, and 0.125,respectively.

In a related set of experiments, the effects of linear ablation on theaverage duration of multi-wavelet reentry were tested. Tissue area was800 mm² and baseline boundary-length-to-surface-area ratio was 0.15prior to simulated ablation. As ablation lines were added to the tissue,the average time to termination of multi-wavelet reentry progressivelydecreased. FIGS. 9A-9C illustrate how ablation lines increase theboundary-length-to-surface-area ratio and decrease the duration ofmulti-wavelet reentry in accordance with some aspects of the presentinvention. In FIG. 9A, zero ablation lines produced termination ofmulti-wavelet reentry 90 in 2.2±2.9×10⁵ time-steps; in FIG. 9B, oneablation line 92 produced termination of multi-wavelet reentry in4.2±8.5×10⁴ time-steps; in FIG. 9C, two ablation lines 94 and 96produced termination of multi-wavelet reentry in 1.6±2.5×10³ time-steps;in FIG. 9D, three ablation lines produced termination of multi-waveletreentry in 575±67 time-steps.

Finally, the effects of heterogeneous tissue properties on theeffectiveness of ablation lesions were tested. When the central area ofthe tissue had shorter average action potential duration (90±15 ms) thanthe surrounding regions (115±10 ms), spiral waves meandered and werepreferentially located within the central short refractory period zone.The mean spiral-wave-tip density (measured as the number of cores perspace-time volume) was significantly higher in the central shorteraction potential duration zone (4.73±0.71 cores/mm² ms) compated to thesurrounding tissue (2.95±0.18 cores/mm² ms), P<0.001. In tissue withouta central short action potential duration zone, there was no significantdifference in spiral-wave-tip density between the central zone and theperiphery (1.58±0.65 vs. 1.57±0.52 cores/mm² ms, P=0.963).

The regional efficacy of ablation for termination of multi-waveletreentry was assessed by delivering ablation lesions either to thecentral zone (high spiral-wave density) or the surrounding tissue (lowspiral-wave density). In both cases, the totalboundary-length-to-surface-area ratio was kept fixed (0.13) by varyingonly the location but not length or number of ablation lines. Onehundred percent of episodes terminated when lesions were deliveredinside the central zone, compared with 76% termination followingablation outside the central zone (n=25). The average time totermination was shorter when lesions were placed within the central zone(1.0±1.2×10⁴ time-steps) compared with lesions placed only in thesurrounding tissue (7.5±8.2×10⁴ time-steps), P=0.0005. Conversely, whenthe tissue periphery had shorter average action potential duration(90±15 ms vs. 115±10 ms), spiral-wave-tip density was higher within thatarea (4.05±0.64 cores/mm² ms) compared with the central longer actionpotential duration zone (3.29±0.52 cores/mm² ms), P<0.001. Ablationresulted in termination of multi-wavelet reentry in 80% of simulations(whether lesions were placed in the central zone (n=25) or in theperiphery (n=25)). The average time to termination was shorter whenlesions were placed in the peripheral high spiral-wave-tip density zone(1.7±2.8×10⁴) compared with the central low spiral-wave-tip density zone(4.9±3.7×10⁴ time-steps, P=0.009).

The framework presented here offers a perspective for understandingtreatment of multi-wavelet reentry—when it succeeds and when it fails.Anti-arrhythmic medications alter atrial functional topology andablation alters atrial structural topology. The requirements forrendering atrial functional topology incapable of supporting reentry areprescribed by the framework of circuit interruption/innerboundaryelimination. The pragmatic realization of this goal in the complexfunctional and structural architecture of the atria is a tremendouschallenge.

In multi-wavelet reentry spirals terminate when all spiral-cores collidewith an outer boundary. The probability of collision, and thereforetermination, is increased as the ratio of total boundary length to areais increased. The addition of linear ablations (contiguous with thetissue edge) can substantially increase the probability of termination.Ablation lines are most likely to result in termination of multi-waveletreentry when delivered to areas of high spiral-wave density.Interestingly, the addition of linear scar resulted in increaseddispersion of refractoriness (through reduced electrotonic interactions,data not shown). Although this alone enhances the propensity forreentry, because scars were contiguous with an outer boundary they didnot provide a circuit and hence were not arrhythmogenic.

The key question, then, is where to place additional lesions in order tooptimally treat the significant of patients not responsive to currentstrategies. This topological framework guides us in answering thisquestion, the goal being to distribute linear lesions that provide thegreatest likelihood of producing wave extinction while at the same timeminimizing total lesion length.

The framework also helps to shed light on some controversial aspects ofatrial fibrillation ablation. For example, there are numerous reports ofimproved outcome with addition (or sole use) of focal ablation thattargets complex fractionated atrial electrograms. On the basis of thefindings in this study, one would predict that focal ablation wouldcreate new potential reentrant circuits (unless lesions are continued toan atrial boundary).

Ultimately, it is desirable to apply this topological analysis toindividual patients to prospectively identify those requiring additionalablation lesions and to design optimal ablation strategies that arepatient specific. This has not been possible prior to the presentinvention and its embodiments.

Mass Hypothesis of Cardiac Fibrillation

The propensity of a tissue to maintain fibrillation is proportional toits area. However, total surface area is not the only determinant offibrillogenicity. Fibrillation terminates more quickly in long, skinnystrips of tissue compared with square tissue of the same total area. Itwas this observation that led to the recognition that cardiacfibrillation is a reentrant rhythm requiring a minimum radius withinwhich to turn around. Using this approach, atrial fibrillation shouldnot be maintained if the tissue substrate is divided into segments toosmall to allow a reentrant circuit. Using computer modeling studies,this approach was expanded based on the recognition that multi-waveletreentry terminates when rotor cores collide with a tissue outer boundaryand that collision is more likely as the ratio of tissue boundary totissue area is increased (e.g., through addition of linear ablationlesions contiguous with the tissue edge). It was further recognized thatwhen the distribution of rotor cores is concentrated in certain regions(based upon tissue physiology and architecture), the probability ofcollision is greatest when ablation lines are placed in the regions withhigher rotor density.

Evolutionary Hypothesis of Ablation Lesion Placement

In a study, a Covariance Matrix Adaptation Evolutionary Strategy(“CMA-ES”) was used to “evolve” an optimized distribution (location,orientation, and length) ablation lesions for preventing, minimizing,and or terminating cardiac fibrillation. Optimization or fitnessfeedback was based upon the extent to which these proposed ablationlesions decreased the ability of the cardiac tissue substrate to induceand sustain multi-wavelet reentry. The characteristics of the evolvingablation lesion sets were assessed with regard to their adherence to theprinciples outlined by the conceptual strategy, specifically: (1) thepercent of lines that are contiguous with the tissue's outer boundary;and (2) the total contiguous tissue area (i.e., the amount of tissue notelectrically isolated (quarantined) by enclosing ablation lesions).

In order to test whether the CMA-ES would identify the strategy ofconcentrating ablation lines in regions of higher circuit density,ablation lines were evolved under at least one of two conditions: (1)“homogeneous” simulated tissue in which circuits were uniformlydistributed (i.e., the control condition); and (2) “heterogeneous”simulated tissue containing a patch of tissue with a higherconcentration of circuits then the remainder of the tissue.

A computational model was used to generate simulated two-dimensionaltissue sheets, comprised of an array of (e.g., 60×60) “cells.” Each cellrepresents a large number of myocytes. The intercellular resistance wasuniform in each direction and throughout the tissue (unless otherwisestated). The action potential duration (and refractory period) of eachcell varied randomly throughout the tissue with a mean of 100±25 ms. Thecells properties included restitution; action potential duration wasrate-dependent (varying as a function of preceding diastolic interval).In homogeneous tissue the distribution of baseline action potentialduration (prior to the effects of restitution) was randomly selectedproducing a relatively uniform concentration of circuits across thetissue when following induction of multi-wavelet reentry was induced. Inheterogeneous tissue the action potential duration of cells within apatch of tissue (20×20 cells located along the middle third of thetissue border) was set to vary about a mean of 50±25 ms. Theinter-cellular resistance within this patch was increased by 140%relative to the tissue outside the patch. In each case (homogeneous andheterogeneous) 10 separate replicates of macroscopically similar tissueswere generated which had unique (random) distributions of actionpotential duration (using the same mean and standard deviation).

FIGS. 10A-10B illustrate the circuit density across simulated tissue inaccordance with some aspects of the invention. In FIG. 10A, thedistribution is homogenous; however, in FIG. 10B, the distribution isheterogeneous.

Multi-wavelet reentry was generated using cross field stimulation. Inthe baseline state the duration of induced multi-wavelet reentry isassessed, if termination occurred within the 2.5 second simulation thetissue is was rejected and a new tissue generated. This process wasrepeated until 10 acceptable test tissues were generated.

Circuits were identified by first converting the space-time plots oftissue voltage to phase maps using a Hilbert transform. Phasesingularities were identified as sites at which (1) all phases meet at asingle point and (2) phases are arranged in sequence from −Π to Π. Inorder to eliminate false positive phase singularities (those notidentifying a rotor core), the leading edge of each wave was delineated(based upon initiation of AP upstroke). Phase singularities that werenot located at the end of a wave-front were eliminated.

Evolutionary algorithms are biologically inspired solution-space searchmethods. In general such algorithms involve: (1) randomly creating apopulation of candidate solutions; (2) assessing the fitness of thesesolutions relative to a fitness function or criterion; (3) selecting atleast one of fittest solutions; and (4) creating a new generation ofcandidate solutions through some process of varying the priorgeneration's selected solution(s). These steps are iterated resulting inprogressive optimization of the solutions' fitness. CMA-ES is one ofmany different types of evolutionary algorithms that may be appropriatefor lesion optimization. CMA-ES is designed to optimize real valuedfunctions of real-valued vectors. For example one might seek areal-valued vector z that minimizes y in the fitness function ƒ.ƒ(z1,z2, . . . ,zn)=y  (1)

The fitness function may be non-differentiable, non-linear andnon-convex; CMA-ES treats the function as a black box. In our case zcorresponds to a set of ablation lines and ƒ is a fitness functiondesigned to optimize the ability of those lines to terminate andpreclude multi-wavelet reentry.

CMA-ES works by naturally following the contours of a co-evolvingestimate of the surrounding fitness landscape in seeking to improve asingle current solution estimate. Rather than maintaining a fixedpopulation size as in many evolutionary algorithms, CMA-ES starts byassuming a multivariate normal distribution around a single randomlyselected solution vector m with covariance C, which is initially assumedto be a diagonal matrix (i.e., uncorrelated variables in solution space)with a pre-defined global standard deviation σ. It then proceeds toco-evolve improved estimates of the solution (new mean m) and animproved estimate of the covariance matrix C of the variables insurrounding solution space, as follows.

For every generation: (1) a population cloud of λ potential solutions isgenerated according to the current estimate of the multivariate normaldistribution described by C around the solution vector m; (2) thispopulation is then truncated to the best μ solutions, where μ istypically on the order of one half λ; (3) a fitness-weighted average ofthe remaining μ solutions becomes the new m, thus reducing thepopulation to only one candidate solution; and (4) the covariance matrixC is updated using local fitness landscape information based on thegenerational change in m (a rank 1 update), the most recent μ samples ofthe solution space in the vicinity of m (a rank μ update), and thelength of evolution path of successive estimates of m. As the searchnears an optimum, the variance estimates approach zero and CMA-ESconverges. Multiple random restarts of CMA-ES can be used to avoidgetting stuck in local optima. To apply CMA-ES one must define anencoding for the solutions and a function to measure fitness.

The encoding defines how a real vector z maps to a solution, in thiscase a set of six ablation lines. Ablation lines are represented by avector of 24 real numbers bounded from [−1; 1]:z=[x1,y1,x2,y2, . . . ,x12,y12]  (2)The successive pairs of values are interpreted as (x, y) Cartesiancoordinates. Each coordinate pair defines the endpoints of a singlestraight ablation line, so there are six lines for each ablation set.Any cell i that falls underneath an ablation line is set to “dead”(unexcitable) and has an infinite resistance with its neighbors. Allpotential solutions (m and the clouds of λ potential solutions createdeach generation) are of this form.

The initial ablation sets were explicitly biased to discourageconnections of ablation lines to an exterior boundary, in order to seeif such connections would reliably evolve. All values in the initialvector m that encodes ablation sets are drawn from a uniformdistribution [−0.4, 0.4]. The initial standard deviation σ is 0.2, hencethe initial covariance matrix estimate is:

$\begin{matrix}{C = \begin{bmatrix}\sigma^{2} & 0 & 0 \\0 & \ddots & 0 \\0 & 0 & \sigma^{2}\end{bmatrix}} & (3)\end{matrix}$or α²I. These parameters ensure that 95% of the ablation lines in theinitial population are within the range of [−0.8, 0.8], thus they tendnot to connect to an exterior boundary.

Tissue activation frequency, FR, is defined as the mean activationfrequency of all the cells:

$\begin{matrix}{{FR} = {\frac{1}{TN}{\sum\limits_{i = 1}^{N}s_{i}}}} & (4)\end{matrix}$where s_(i) is the number of activations of the ith cell, N is the totalnumber of cells, and T is the number of seconds the tissue is simulated(2.5). The units of FR are activations per second. An FR of 1 meanscells on average are activated once per second.

Our CMA-ES minimizes the fitness function:

$\begin{matrix}{{{f(x)}F} = {\frac{1}{10}{\sum\limits_{j = 1}^{N}{FR}_{j}}}} & (5)\end{matrix}$where F is the mean activation frequency FR of ten training tissues. Twoconstraints are imposed on the ablation sets: (1) the total number ofablated cells cannot exceed 20% of the tissue; and (2) no more than 18%of the tissue can be quarantined. Any ablation set that violates theseconstraints is eliminated and replaced until an ablation set thatsatisfies the constraints is produced.

Population sizes of λ=15 and μ=7 were selected based on the genome sizeof 24. The CMA-ES was run for 200 generations (before which the rate offitness improvement had diminished). For each evolutionary run, fitnesswas evaluated on ten randomly generated training tissues of a given type(homogeneous or heterogeneous) exhibiting MWR, and the resultingfitness's were averaged. By testing on 10 different tissues with varieddistribution of similar electrophysiologic parameters the evolvedsolutions were general to a “type” of tissue rather than a specificindividual tissue.

Each lesion set was assigned characteristics, including percent oflesions contiguous with an outer boundary, percent quarantine, andboundary-length-to-surface-area ratio. The proportion of ablated cellsthat connect to a tissue boundary was defined as pC. If all ablatedcells ultimately connect to a boundary, pC=1. If the ablated cells forman island never connecting to an edge, pC=0.

If ablation lines enclose a region of the tissue the enclosed cellsbecome electrically isolated from the remainder of the tissue,effectively reducing the tissue area. The proportion of cells isolatedby ablation is defined as pQ. If a tissue were ablated with a lineextending from the top center of the tissue to the bottom center then pQwould equal 0.5.

Let pA be the proportion of cells that are ablated. The length of theexterior boundary L is the total number of ablated cells connected tothe exterior boundary (N pA pC) plus the exterior boundary (B) (which is240=60×4 for a 60×60 tissue bounded on its four sides). The contiguouselectrically excitable tissue area A is the total number of cells Nminus the ablated cells, pA, and the quarantined cells, pQ. To test thehypothesis that the probability of multi-wavelet termination is directlyproportional to the exterior boundary length and inversely proportionalto the tissue surface area, the following ratio was calculated:

$\begin{matrix}{\frac{L}{A} = \frac{{{N \cdot p}\;{A \cdot {pC}}} + B}{N\left( {1 - {p\; A} - {p\; C}} \right)}} & (6)\end{matrix}$

To determine the contribution of boundary continuity to the fitness ofeach final evolved set of ablation lines we retested their fitness afterdisconnecting them from the tissue edge. The last two ablation lesions(points) connecting the line to the tissue boundary are “un-ablated” sothat no ablation lines connect to the exterior boundary and pC=0.

Two sets of experiments were run with ten independent evolutions each.In the first, ablation lesion sets were evolved on homogeneous tissues.In the second, ablation lesion sets were evolved on tissue containing apatch of cells with shorter wave length (refractory period×conductionvelocity) due to reduced action potential duration and increasedintercellular resistance. In the latter heterogeneous tissues, weconfirmed that there was increased circuit density in the shortwave-length patch.

In the first set of experiments, the following were examined: (1) theproportion of ablation lines contiguous with the exterior boundary pC;(2) the amount of quarantined tissue pQ; (3) the length to area ratioL/A (i.e., the total exterior boundary length, including ablation linesdivided by the contiguous tissue area excluding quarantined tissue); and(4) the fitness FR. The results (mean±standard error of the mean (SEM))are presented in FIG. 11, which is a plot of ablation lesioncharacteristics and fitness in tissue with homogeneous circuit densityin accordance with some aspects of the present invention. Fitnessimproves as lesions evolve (0.93±0.12 to 0.07±0.01 p<0.001). Thepercentage of ablation points contiguous with the exterior boundarysteadily increases (0.01±0.02 to 0.99±0.02, p<0.001). The total lesionlength also increases to the maximum allowable of 18% (0.00±0.00 to0.15±0.03, p<0.001). The proportion of quarantined tissue alsoincreases. The net result is an increase in thebounday-length-to-surface-area ratio (0.07±0.00 to 0.20±0.01, p<0.001).

As the total length of ablation lines contiguous with the exteriorboundary (L) decreases, hat ablation set was expected to be less likelyto terminate multi-wavelet reentry. To test this hypothesis, in each ofthe best evolved ablation sets, the last two ablation points connectinga line to the tissue edge were “unablated” and fitness retested. Ten newtest tissues (that were not used during training) exhibiting MWR weregenerated to re-evaluate each modified ablation set. Prior to modifyingthe ablation sets, the average pC=0.99±0.02, the average L/A=0.20±0.01,and the average fitness FR=0.90±0.03 (mean±standard error). Followingablation modification (disconnection from outer boundaries), the averagepC=0±0, the average L/A=0.08±0.001, and the average pT=0.23±0.04.

In a second set of experiments, the ablation sets that evolved inheterogeneous tissue (with a high circuit density patch) were examined.The density of ablation lesions in the top middle portion of the tissue(high circuit density patch) were compared with that in the remainder ofthe tissue. Ablation density was higher in the patch than in theremainder of the tissue (0.08±0.01 vs 0.15±0.01, p<0.001). FIG. 12A is aplot of ablation density versus circuit density for tissue without ahigh circuit density patch, in accordance with some aspects of thepresent invention. In contrast, the ablation density was the same in andoutside of the top middle portion of the tissue in the homogeneoustissue experiments. FIG. 12B is a plot of ablation density versuscircuit density for tissue with a high circuit density patch, inaccordance with some aspects of the present invention. Ablation densityis markedly increased in the high circuit density region.

Based upon an explanatory model for propagation through excitabletissue, multi-wavelet reentry necessitates complete circuits for itsperpetuation. This implies the strategy for its ablation: interruptthese circuits causing termination. Interruption requires completecircuit transection thus the first tenet of the conceptually-guidedstrategy: lines must be contiguous with the tissue's exterior boundaryand extend to the circuit-core. To corroborate this principle using theCMA-ES a first generation of ablation lines was created that were notcontiguous with an outer boundary so that if the evolved ablationstrategies had a greater percentage of lines connected to the outerboundary than would result from random mutation, fitness pressure forsuch connection must be at work. Starting from an initial generation inwhich virtually none of the lines were contiguous with the tissue'souter boundary (by design), by the end of evolution nearly 100% of lineswere connected.

To confirm that it was continuity with the boundary that conferredincreased fitness, the ends of each ablation line were eliminated attheir point of contact with the boundary. In each case the fitnessdecreased when lines were disconnected from the outer boundary.

If collision is fundamental to efficacy then lines in areas with highercircuit density, where collision is more likely, should be moreeffective than those in areas with lower density. To test whetherfitness pressure would drive ablation lines toward areas of high circuitdensity solutions were evolved on tissue with a patch of increasedcircuit density. In each evolution performed on heterogeneous tissue,ablation lines were concentrated within the high circuit-density patch.In contrast, the density of ablation lines in the same tissue region wasnot increased when evolved on homogeneous tissue.

The current results help to validate the fundamental principles thatunderlie the conceptually-guided strategy. The two approaches tosearching the solution space of the ablation problem (evolutionaryalgorithmic and conceptually-guided) are fundamentally different andnon-derivative. The fact that in each case the lesion sets adhere to thesame principles (due to fitness pressure on the one hand and bymechanistically-inspired design on the other) supports the importance ofthese tenets. This is critical because an evolutionary approach does notapply in human hearts (only a single lesion set may be delivered). Thekey characteristic of the conceptually-guided approach is that iteffectively allows for a priori efficacy evaluation (through mentalmodeling) so when ablation lesions are delivered they have already been“tested”.

In modern science there has been a growing appreciation of the existenceand nature of complex systems. Such systems, comprised of multiple partsinteracting in non-linear fashion, are capable of extremely complexbehaviors. The heart is such a system. It has a very simple jobdescription: it must pump blood. The achievement of this task, however,is tremendously complex requiring the coordinated activity of billionsof ion channels in millions of cells interacting electrically andmechanically in an elegant symphony, and without the benefit of aconductor. When functioning normally the heart sustains life, whensufficiently deranged it precludes it.

In the context of multi-wavelet reentry, ablation amounts tomanipulating the structure of a complex non-linear system so as toconstrain its behavior. Even if we limit allowable manipulations to theplacement of ablation lines, the number of possible solutions is vastand exhaustive search is intractable.

Measurements Indicative of the Fibrillogenicity of a Cardiac TissueSubstrate

Fibrillogenicity is a measure of how conducive a patient's heart is tosupporting fibrillation. A fibrillogenicity assessment allows aclinician to estimate the amount of ablation (e.g., the total length ofablation lesions) that will be required to treat and minimizefibrillation in a particular patient.

The relationship between a patient's fibrillogenicity and physiologicfactors may be represented as, for example:

$\begin{matrix}{{FB} \propto \frac{A}{L}} & (7)\end{matrix}$where FB is fibrillogenicity, A is the surface area of the tissuesubstrate, and L is the boundary length of the substrate. As shown inthe equation above, fibrillogenicity may be considered proportional tothe ratio of surface area to boundary length of the tissue substrate.

Fibrillogenicity also may be considered inversely proportional to thetissue excitation wavelength k:

$\begin{matrix}{{FB} \propto \frac{1}{\lambda}} & (8)\end{matrix}$As discussed above, a reentrant circuit will be interrupted if thetissue excitation wavelength exceeds the circuit length. The tissueexcitation wavelength is the distance from the leading edge of a tissueexcitation wavefront to its trailing edge of unexcitable refractorytissue. As tissue excitation wavelength increases, fewer reentrantcircuits can be supported per unit area of tissue substrate. Thus,fibrillogenicity may be considered proportional to the number ofreentrant circuits the tissue is capable of supporting per unit area.

Ideally, an assessment of a patient's fibrillogenicity should take intoaccount measurements (even if only indirect indications are available)of the substrate surface area (e.g., the patient's atrial surface area),the total boundary length of the substrate (e.g., the patient's atrialboundary length), and the minimum substrate area required to support onereentrant circuit.

Minimum Circuit Area

The minimum substrate area required to support one reentrant circuitinforms the extent of electrical derangement in the tissue. The measureof the area of tissue required to support an individual rotor is theminimum circuit area. As the minimum circuit area decreases, the tissuesubstrate as a whole becomes capable of supporting more rotors, and theprobability that all circuits will be interrupted simultaneously andfibrillation will terminate. Thus, fibrillogenicity increases as theminimum circuit area decreases.

However, the determinants of minimum circuit area are multifactorial andmany of the factors are emergent (i.e., the result of interactionsbetween cell physiology, tissue anatomy, and the evolving circumstancesof global and local activation states). While the minimum circuit areacannot be measured directly, the minimum circuit area is related, atleast in part, to the tissue excitation wavelength.

Tissue excitation wavelength is not a single static parameter of tissuebut a product of the conduction velocity of a wave and the refractoryperiod (i.e., the amount of time required to recover excitabilityfollowing excitation) of the tissue through which the wave is traveling.Both of these factors depend upon spatiotemporal context. For example,the refractory period of cardiac tissue varies with the frequency atwhich a given heart cell is excited. A given heart cell is excited atfrequencies that tend to range from 4 to 15 Hz, particularly 5 to 10 Hz.Meanwhile, the conduction velocity of a wave is influenced by waveshape: curved waves (e.g., rotors) conduct more slowly than flat waves.Hence, tissue excitation wavelength—and thus minimum circuit area—mayvary over time and across the heart, even in an individual patient.

Electrocardiography (“ECG/EKG”) may be used to gather measurementsindicative of tissue excitation wavelength and thus minimum circuit areaby recording the electrical activity of a patient's heart at the bodysurface. An electrocardiograms (also a “ECG/EKG”) translates theelectrical deflections or changes in the electrical potential producedby the contractions of a heart into graphical waveforms. During anatrial fibrillation episode, for example, the ECG/EKG may showfibrillatory waves (“F-waves”), which are small, irregular, rapiddeflections. The wavelength of F-waves in a patient may be consideredproportional to, and thus indicative of, tissue activation wavelengthand minimum circuit area. As described above, these measurementscorrelate with a patient's fibrillogenicity and, consequently, may beincorporated into the estimation of how much ablation is needed and/orwhether an ablation procedure is complete.

Boundary-Length-to-Surface-Area Ratio

Fibrillogenicity is also modulated by the total boundary length of thetissue substrate, which, for an atrium, is the sum of the circumferencesof the atrial boundaries and orifices (e.g., the superior vena cava,inferior vena cava, atrioventricular tricuspid valve, atrioventricularmitral valve, and orifices of the pulmonary veins). As described above,reentrant circuits terminate upon complete interruption. A completeinterruption requires the absence of a continuous path of excitabletissue at any point in the reentrant circuit. A moving circuit may causeits own interruption when its core collides with a physical boundary.Thus, the core of a moving circuit may interrupt the circuit itself bymeandering into a tissue boundary or orifice In the context of movingcircuits, the probability of such a collision increases with the totallength of any boundaries. Therefore, total boundary length may beconsidered inversely proportional to fibrillogenicity.

FIG. 63A-63B are computer axial tomography scans of a human heart. FIG.63A is a right atrium with boundary/orifice 631. FIG. 63B is a leftatrium having three boundaries/orifices 632, 633, and 634. To calculatethe total boundary length of the tissue substrate, add the sum of thecircumferences of the atrial boundaries and orifices shown in FIGS. 63Aand 63B. The total surface area is calculated by removing the area ofthe boundaries/orifices from the surface area of the tissue substrate.

Meanwhile, as the surface area of a tissue substrate (e.g., the atrialsurface area) increases, a moving circuit may have more space to meanderwithout its core colliding with a boundary and interrupting the circuititself. The probability of a such a collision decreases with an increasein total surface area. Therefore, total surface area may be considereddirectly proportional to fibrillogenicity.

Given these multiple relationships, the probability of collision may beincreased by extending the electrical boundaries of tissue substrate bythe interventional placement of ablation lesions connected to existingboundaries (e.g., anatomic boundaries and/or previously created ablationlesions). From another perspective, lesions may be placed to decreasesurface area, thus increasing the probability of collision. Therefore,boundary-length-to-surface-area may indicate (at least in part) anamount or length of boundaries (i.e., lesions) to be added and/or anamount of surface area to be removed, such that the finalboundary-length-to-surface-area ratio favors collision and terminationof fibrillation.

The boundary lengths and surface areas of the heart may be mapped ontoand measured from, for example, a cardiac magnetic resonance imaging(MM) scan, computed tomography (CT) scan, rotational angiogram,three-dimensional ultrasound image, three-dimensional electro-anatomicmap, and/or other medical representation. Once the surface of a tissuesubstrate (e.g., an atrium) is scanned and reconstructed as one or morerepresentations (e.g., two-dimensional images or three-dimensionalmodels) via one of these imaging modalities, the one or morerepresentations may be used to measure and/or compute boundary lengths,the surface areas, and/or boundary-length-to-surface-area ratios.

Like the minimum circuit area, the boundary-length-to-surface-area ratioprovides a more complete indication of the tissue fibrillogenicity andinforms the extent of ablation required to reduce fibrillogenicity andminimize or prevent further fibrillation. As described below, thisinformation—combined with the density and distribution of circuitcores—may be used to assess and even quantify fibrillogenicity inaccordance with some embodiments of the present invention.

FIG. 13 is a system component block diagram in accordance with certainembodiments of a system for making measurements indicative offibrillogenicity in a patient. The system may include an ECG/EKGsubsystem 501 for collecting measurements indicative of tissueactivation wavelength (and minimum circuit area) and/or an imagingsubsystem 502 for acquiring or collecting measurements indicative of atissue substrate's total boundary length, total surface area, and/orboundary-length-to-surface-area ratio. The system may also include, butis not limited to, a catheter subsystem 503, a processing unit 504, amemory 505, a transceiver 506 including one or more interfaces 507, agraphical user interface (“GUI”) 508, and/or a display 509 (eachdescribed in detail below).

The ECG/EKG subsystem 501 may be used to measure the heart's electricalactivity (e.g., F-waves) as recorded at the body surface. Thesemeasurements correlate with the fibrillogenicity and, consequently, maybe incorporated into the calculus for estimation of how much ablationneeds to be performed (and, as described below, whether or not anablation procedure is complete). The ECG/EKG subsystem 501 may include aseparate display and/or share a display 509 with other components of thesystem shown in FIG. 13. The ECG/EKG subsystem 501 and its componentsmay be operated manually and/or automatically.

The imaging subsystem 502 may include any means by which a medicalrepresentation (e.g., a two-dimensional image or three-dimensionalmodel) of a tissue substrate is acquired and/or generated, allowing themeasurement of, for example, an atrium's surface area along with theveins and valves (i.e., boundaries) that interrupt its surface. Suitableimaging modalities include, but are not limited to, MRI, CT, rotationalangiography, three-dimensional ultrasound, and/or three-dimensionalelectro-anatomic mapping. Some imaging modalities may require theinjection of one or more contrast agents. The imaging subsystem 502 mayinclude a separate display and/or share a display 509 with othercomponents of the system shown in FIG. 5. The imaging subsystem 502 andits components may be operated manually and/or automatically.

A electrophysiological study was undertaken to investigate whichclinical variables, including a noninvasive measurement of cycle lengthfrom a surface ECG/EKG, are predictive of a successful procedural andmedium-term clinical outcome using a sequential catheter ablationapproach in patients with persistent cardiac fibrillation. Ninetypatients, who underwent first-time radiofrequency catheter ablation forlong-lasting persistent cardiac fibrillation, were included in thestudy. Long-lasting persistent cardiac fibrillation was defined ascontinuous cardiac fibrillation lasting longer than one month andresistant to either electrical or pharmacological cardioversion.

Surface ECG/EKG and endocardial electrograms were continuously monitoredduring the ablation procedure and recorded for off-line analysis. Thesurface ECG/EKG cycle length was compared with the endocardial cyclelength obtained simultaneously from the intracardiac recordings at boththe left atrial appendage and the right atrial appendage beforeablation. In all patients, the surface ECG/EKG cycle length was manuallymeasured from 10 unambiguous fibrillatory waves on lead V₁ (minimalvoltage>0.01 mV) that were not fused with QRST segments at a paper speedof 50 mm/s and a gain setting of 20, 40, or 80 mm/mV. FIG. 14 is a plotof simultaneous measurements of the atrial fibrillatory cycle lengthfrom surface ECG/EKG and the left and right atrial appendages accordingto some aspects of the present invention. Seiichiro Matsuo et al.,“Clinical Predictors of Termination and Clinical Outcome of CatheterAblation for Persistent Atrial Fibrillation,” 54:9 J. of Am. College ofCardiology 788-95 (2009). In FIG. 14, the cycle lengths from surfaceECG/EKG, left atrial appendage (“LAA”), and right atrial appendage(“RAA”) were 139 ms, 144 ms, and 145 ms, respectively. Id.

In the first 30 patients, intraobserver and interobserver error of thesurface ECG/EKG cycle length from 10 cycle lengths was assessed. Thesurface ECG/EKG cycle length from 10 cycle lengths was measured on twodifferent days and using two independent experts, respectively. The meansurface ECG/EKG cycle length from 10 cycle lengths was compared withthat from 30 cycle lengths (manually measured) and with the mean cyclelength using automated time frequency analysis of 60 s of simultaneoussurface ECG/EKG recording. Digital measurement of fibrillatory ratesusing time frequency analysis was disqualified because of poor signalquality in 4 patients.

In all patients, sequential stepwise ablation was performed, involvingpulmonary vein isolation, electrogram-based ablation, and linearablation. Ablation around the pulmonary veins was performed with the aidof a Lasso catheter. The end point of this step was the elimination ordissociation of the pulmonary vein potentials as determined by a Lassocatheter in all veins. Isolation of the pulmonary veins was confirmedafter restoration of sinus rhythm. After this, electrogram-basedablation was performed at sites in the left atrium showing any of thefollowing electrogram features: continuous electrical activity, complexrapid and fractionated electrograms, and a gradient of activation (atemporal gradient of at least 70 ms between the distal and proximalbipoles on the roving distal ablation electrode, potentiallyrepresenting a local circuit). Linear ablation in the left atrium wasperformed if atrial fibrillation persisted after electrogram-basedablation. A roof line was performed joining the right and left superiorpulmonary veins, and if atrial fibrillation continued, a mitral isthmusline from the mitral annulus to the left inferior pulmonary vein wasperformed. After restoration of sinus rhythm, assessment of conductionblock across the lines was performed in all patients with supplementaryablation, if necessary, to achieve block. A cavotricuspid isthmus linewas performed in all patients with an end point of bidirectional block.

The procedural end point was termination of longlasting persistentatrial fibrillation by catheter ablation, either by conversion directlyto sinus rhythm or via one or more atrial tachycardias, which weresubsequently mapped and ablated. When atrial fibrillation was notterminated by ablation, it was terminated by electrical cardioversion.After cardioversion, if necessary, supplemental radiofrequency energywas delivered to establish pulmonary vein isolation and conduction blockof any linear lesion. Clinical outcome of long-lasting persistent atrialfibrillation ablation. Success was defined as maintenance of sinusrhythm without antiarrhythmic drug treatment more than 12 months afterthe final procedure. Failure was defined as documented recurrence ofatrial fibrillation or atrial tachycardia lasting for more than 3 min.

Patients were hospitalized for between 3 and 5 days post-procedure andseen at 1, 3, 6, and 12 months for clinical interview, echocardiography,and 24-hour ambulatory monitoring in addition to routine follow-up bythe referring cardiologist. One year from the last procedure, patientswere seen every 6 months by their referring cardiologist. All patientsunderwent 24-hour Holter monitoring within the last 3 months offollow-up. Antiarrhythmic medication was continued for 1 to 3 monthsafter the index procedure, and anticoagulation treatment was continuedfor at least 6 months. A repeat ablation procedure was undertaken in theevent of a recurrence of atrial fibrillation or atrial tachycardialasting more than 3 min.

Linear regression analysis was used to test the association between thesurface ECG/EKG cycle length from 10 cycle lengths and 30 cycle lengths,time frequency analysis of a 60-s sample window, LAA cycle length, RAAcycle length, and procedure time. A Bland-Altman plot was generated toexamine the precision between the RAA cycle length and the surfaceECG/EKG cycle length from 10 cycle lengths, 30 cycle lengths, and timefrequency analysis. To evaluate intraobserver and interobservervariability, the Pearson correlation coefficient (r) was calculated forthe surface ECG/EKG cycle length from 10 cycle lengths. Continuousvariables are expressed as mean±standard deviation or median withinterquartile range where indicated. Statistical significance wasassessed using the unpaired Student t test or Mann-Whitney Utest ifnecessary. Categorical variables, expressed as numbers or percentages,were analyzed using the chi-square test or Fisher exact test. To analyzeindependent predictive factors of termination of atrial fibrillationduring ablation and independent factors of clinical success, univariatefactors presenting p<0.1 were analyzed using logistic regression(multivariate analysis). The receiver-operator characteristic curve wasdetermined to evaluate the performance of the best independent predictorof atrial fibrillation termination by catheter ablation. The optimalcutoff point was chosen as the combination with the highest sensitivityand specificity. All tests were 2-tailed, and p<0.05 was consideredsignificant. Cumulative event rates (recurrence of arrhythmia) werecalculated according to the Kaplan-Meier method.

Intraobserver and interobserver correlations were high in themeasurement of the cycle length from the surface ECG/EKG using 10 cyclelengths (R=0.97 and R=0.98, respectively). In the first 30 patients,surface ECG/EKG cycle length was calculated using manual measurement of10 and 30 cycle lengths and the use of time frequency analysis analysisof a 60-second simultaneous recording window. FIG. 15A is a plot showingthe relationship between mean surface ECG/EKG atrial fibrillation cyclelength measurement from 10 and 30 cycle lengths. Id. FIG. 15B is a plotshowing the relationship between surface ECG/EKG cycle length from 10cycle lengths and atrial fibrillation cycle length using time frequencyanalysis. Id. There was a strong correlation between the cycle lengthfrom the surface ECG/EKG measured with 10 and 30 cycle lengths (R=0.984,p<0.0001), plotted in FIG. 15A, and between the surface ECG/EKG cyclelength calculated manually using 10 cycle lengths and digitalmeasurement using time frequency analysis (R=0.941, p<0.0001), plottedin FIG. 15B. Id.

The mean surface ECG/EKG cycle length from 10 cycle lengths and LAA andRAA cycle length of the total population were 150±19 ms, 153±20 ms, and157±20 ms, respectively. The mean surface ECG/EKG cycle length waslonger in patients taking amiodarone (163±18 ms vs. 146±16 ms,p<0.0001). The mean differences between the surface ECG/EKG cycle lengthfrom 10 cycle lengths and the endocardial cycle length in the LAA andRAA were 7±6 ms and 8±8 ms, respectively. FIG. 15C is a plot showing therelationship between surface ECG/EKG atrial fibrillation cycle lengthfrom 10 cycle lengths and the LAA cycle lengths. Id. FIG. 15D is a plotshowing the relationship between surface ECG/EKG atrial fibrillationcycle length from 10 cycle lengths and the RAA cycle length. Id. Thesurface ECG/EKG cycle length from 10 cycle lengths was stronglycorrelated with both the LAA cycle lengths (R=0.893, p<0.0001), plottedin FIG. 15C, and the RAA cycle lengths (R=0.876, p<0.0001), plotted inFIG. 15D. Id.

FIGS. 16A-16C are Bland-Altman plots in accordance with some aspects ofthe study and the present invention. Id. The plot in FIG. 16A shows goodagreement between the RAA cycle lengths versus the cycle length fromtime frequency analysis. Id. The plot in FIG. 16B shows good agreementbetween the RAA cycle lengths versus the manual measurement surfaceECG/EKG cycle length from 30 cycle lengths. Id. The plot in FIG. 16Cshows good agreement between the RAA cycle lengths versus the manualmeasurement surface ECG/EKG cycle length from 10 cycle lengths. Id.

Long-lasting persistent atrial fibrillation was terminated by ablationin 76 of 90 patients (84%), with a mean procedure time of 245±70 min.Pre-procedural clinical variables were compared in patients in whomatrial fibrillation was terminated by ablation versus in those who werenot. Compared with patients in whom atrial fibrillation was notterminated, patients with atrial fibrillation termination had asignificantly shorter duration of continuous atrial fibrillation (22±24months vs. 60±44 months, p<0.0001), a longer surface ECG/EKG cyclelength (154±17 ms vs. 132±10 ms, p<0.0001), and a smaller left atriumdimension (47±7 mm vs. 54±11 mm, p<0.01).

Using multivariate analysis, the surface ECG/EKG cycle length was theonly independent predictor of atrial fibrillation termination bycatheter ablation (p<0.005). There was a trend toward duration ofcontinuous atrial fibrillation predicting atrial fibrillationtermination (p<0.08), but left atrium dimension was not an independentpredictor.

FIG. 17 is a plot showing the receiver-operator characteristic curve forthe surface ECG/EKG cycle length as a predictor of termination oflong-lasting persistent atrial fibrillation in accordance with someaspects of the invention. Id. The area under the receiver-operatorcharacteristic curve of 0.880 (95% confidence interval: 0.795 to 0.939,p<0.0001). As shown in FIG. 17, a cutoff point of 142 ms of the cyclelength had a specificity of 92.9% and a sensitivity of 69.7% inpredicting procedural termination of persistent atrial fibrillation. Id.The positive and negative predictive value of the cycle length 142 mswere 98.1% and 36.1%, respectively, for procedural termination ofpersistent atrial fibrillation. There was an inverse relationshipbetween procedural time and the surface ECG/EKG cycle length (R=0.55,p<0.0001). For the association between the duration of continuous atrialfibrillation and procedural termination, the area under thereceiver-operator characteristic curve was calculated to be 0.844 (95%confidence interval: 0.752 to 0.912, p<0.0001). As shown in FIG. 17, theoptimal cutoff point for the duration of continuous atrial fibrillationwas 21 months for atrial fibrillation termination (specificity 92.9%,sensitivity 61.8%). Id. The combined cutoff using a surface ECG/EKGcycle length >142 ms and a duration of continuous atrial fibrillation<21 months had 100.0% specificity in predicting procedural terminationof persistent atrial fibrillation (sensitivity 39.5%, positivepredictive value 100.0%, negative predictive value 23.3%).

After the final procedure, 84% (76 of 90) of patients were in sinusrhythm without antiarrhythmic drug treatment during follow-up of 18 6months (median 18 months, interquartile range 12 to 24 months). Therewas no difference in total number of procedures between patients withand without recurrence (1.8±0.8 vs. 1.9±0.9, p=NS). The duration ofcontinuous atrial fibrillation (57±54 months vs. 23±21 months, p<0.0001)and the surface ECG/EKG cycle length were longer (154±18 ms vs. 136±11ms, p<0.001) in patients with recurrence of arrhythmia than in those whomaintained sinus rhythm without antiarrhythmic drugs. The dimension ofthe left atrium was smaller (48±8 mm vs. 53±8 mm, p<0.05) in patientswith a successful medium-term outcome. There was a trend toward lowerleft recurrence after the final ablation (53±10% vs. 60±14%, p<0.08).

FIGS. 18A-18B are plots of Kaplan-Meier curve analyses in accordancewith some aspects of the invention. Id. The plot in FIG. 18A shows aKaplan-Meier curve analysis of the incidence of recurrent arrhythmiaafter the last procedure in patients with or without the cycle lengthfrom surface ECG/EKG>142 ms. Id. The plot in FIG. 18A shows aKaplan-Meier curve analysis of the incidence of recurrent arrhythmiaafter the last procedure in patients with or without the duration ofpersistent atrial fibrillation >21 months. Id. In multivariate analysis,the surface ECG/EKG cycle length and the duration of continuous atrialfibrillation independently predicted clinical outcome of persistentatrial fibrillation ablation (p<0.01 and p<0.05, respectively). Patientswith a surface ECG/EKG cycle length <142 ms had a significantly higherrate of recurrent arrhythmia (p=0.001, hazard ratio: 6.0, 95% CI: 2.0 to18.5), as shown in FIG. 18A. Additionally, arrhythmia recurrence afterthe final ablation was frequently observed in patients with duration ofcontinuous atrial fibrillation >21 months compared with those withpersistent atrial fibrillation lasting <21 months (p=0.002, hazardratio: 0.13, 95% CI: 0.06 to 0.51), as shown in FIG. 18B. Id.

Recurrence of arrhythmia after the index procedure was observed in 69%(62 of 90) of patients. Recurrence of atrial fibrillation after theindex procedure was observed more frequently in patients with clinicalfailure compared with those with clinical success (93% [13 of 14] vs. 4%[3 of 76], p<0.0001). In the remaining patients with recurrentarrhythmia, atrial tachycardia was observed and was terminated duringthe repeat ablation procedure. Additionally, procedural atrialfibrillation termination during the index procedure was associated withclinical success (92% [70 of 76] vs. 43% [6 of 14], p<0.0001).

Multivariate analysis showed that the surface ECG/EKG cycle lengthindependently predicts procedural termination using the sequentialstepwise approach. Furthermore, patients with a longer surface ECG/EKGcycle length and a shorter duration of continuous atrial fibrillationhave a better outcome of catheter ablation. Validation of cycle lengthfrom surface ECG/EKG. The surface ECG/EKG cycle length manually assessedfrom 10 cycle lengths correlated well with the cycle length recorded byintracardiac catheters in the LAA and RAA, and using time frequencyanalysis showed that cycle length can reliably be assessed from lead V1on the surface ECG/EKG.

The procedural end point in this study was termination of persistentatrial fibrillation, and this was achieved in the majority of patients.This study shows that a longer surface ECG/EKG cycle length, a shorterduration of continuous atrial fibrillation, and a smaller left atriumdimension are predictive of procedural atrial fibrillation termination.A shorter surface ECG/EKG cycle length was associated with longerprocedural times, suggesting that the results are not caused by operatorbias, but by an increased complexity of atrial fibrillation. Althoughcycle length measured from the LAA is correlated with proceduraloutcome, cycle length calculated from the surface ECG/EKG is noninvasiveand can be performed at the initial consultation. The study also showedthat a cycle length 142 ms predicts the outcome of catheter ablation,indicating that surface ECG/EKG cycle length is a powerful predictor ofclinical outcome. The durations of continuous atrial fibrillation andleft atrium dimensions are predictive of maintenance of sinus rhythmafter DC cardioversion.

In the study, the surface ECG/EKG cycle length was measured using acomputer-based system that allows modification of gain and sweep speed.It is sometimes difficult to assess the cycle length on the surfaceECG/EKG using conventional settings, and therefore multiple settings maybe used to get unequivocal fibrillatory waves on the surface ECG/EKG.There were only 2 patients in whom the cycle length was unable to becalculated from the surface ECG/EKG, and the findings are only relevantwhen the cycle length can be calculated. The study was focused onidentifying clinical factors that can be assessed before ablation;however, other potential predictors for atrial fibrillation recurrenceafter ablation, for example, intraoperative parameters including, butnot limited to, procedural termination of long-lasting persistent atrialfibrillation.

Most importantly, the study confirmed that long-lasting persistentatrial fibrillation can be terminated and potentially cured by catheterablation. The surface ECG/EKG cycle length independently predictsprocedural termination of persistent atrial fibrillation, and both thesurface ECG/EKG cycle length and the duration of continuous atrialfibrillation are predictive of clinical outcome. The measurement of thesurface ECG/EKG cycle length and the duration of continuous atrialfibrillation could help with patient selection for catheter ablation oflong-lasting persistent atrial fibrillation.

Cardiac Fibrillation Detection and Mapping

Fibrillation detection and mapping is aimed at identifying the densityand distribution of reentrant circuit cores that are responsible for theperpetuation of fibrillation. For the reasons described in greaterdetail below, electrogram signal frequency may indicate tissueactivation frequency (provided the electrogram recording is of adequatespatial resolution), which is indicative of circuit core density anddistribution. Thus, a patient-specific map of a tissue substrateindicating appropriately acquired electrogram frequencies informs theoptimal placement of ablation lesions to treat fibrillation.

Circuit Core Density and Distribution

The goal of ablation should be the interruption of all reentrantcircuits. A circuit core meandering on the tissue surface is interruptedif it collides with an electrical boundary. As discussed above, one ormore ablation lesions may be created to increase theboundary-length-to-surface-area ratio and, generically, the probabilityof collision. The one or more ablation lesions should be placedcontiguous with existing tissue boundaries to prevent or at leastminimize the formation of a new circuit of reentry.

Importantly, not all ablation lesions increase the probability ofcollision equally. The creation of new boundaries at tissue sites withhigh circuit core density results in a higher probability of collisionthan the creation of new boundaries at tissue sites with low circuitcore density. Therefore, it remains important to identify indicators ofthe number of circuit cores in a given area of tissue substrate (i.e.,the circuit core density) and the arrangement of circuit cores acrossthe tissue substrate (i.e., the circuit core distribution). Appliedassessment of circuit core density and distribution enhances theefficiency of an ablation treatment by maximizing the effectiveness ofnew boundaries while minimizing the extent of harmful lesions.

Tissue Activation Frequency

One challenge to detecting and mapping fibrillation is the ability toidentify circuit core density; however, circuit core density correlateswith tissue activation frequency. Tissue activation frequency is thefrequency of the variation of tissue current, which rises and falls astissue is excited. Tissue activation frequency may indicate a circuitcore and a surrounding area of tissue in 1-to-1 conduction continuitywith that circuit.

To have 1-to-1 conduction continuity, a surrounding area of tissueundergoes excitation whenever a heart cell at one tissue site is excitedor activated (e.g., by a reentrant circuit). Two tissue sites do nothave 1-to-1 conduction continuity if some degree of conduction blockprevents an excitation from traveling from one tissue site to the other.All heart cells in a reentrant circuit path must have 1-to-1 conductioncontinuity; otherwise, the circuit will be interrupted, and the rotorextinguished. Alternatively, a patient may develop multi-wavelet reentry(i.e., wave break and new wave formation) if 1-to-1 conductioncontinuity does not exist across the tissue. Because tissue activationfrequency identifies surrounding tissue with 1-to-1 conductioncontinuity in addition to the actual tissue site of the circuit core,detection and mapping of tissue activation frequencies alone may notalways accurately indicate circuit core density and distribution (i.e.,tissue activation frequency is overinclusive). However, even so,knowledge of tissue activation frequencies may be applied to enhance theeffectiveness and efficiency of ablation treatments.

Consider that tissue activation frequencies may vary over time as wellas across the surface of a tissue substrate. For example, rotors and therefractoriness of a tissue area may shift (due, e.g., to autonomictone), resulting in new conduction blocks and changing tissue activationfrequencies across the tissue substrate.

Even though the actual tissue site of a circuit core and its 1-to-1conduction continuity area may have the same tissue activation frequencyfor a short time period (e.g., a few seconds), shifts in rotors and therefractoriness of tissue areas over longer periods of time exhibit atendency for tissue activation frequencies to be higher at actual tissuesites of circuit cores than in transient 1-to-1 conduction continuityareas.

Electrogram Signal Frequency

Another challenge to detecting and mapping fibrillation is measuringtissue activation frequency, which cannot be done directly. Thus,instead of tissue activation frequency, measurements of electrogramsignal frequency are used to indicate circuit core density anddistribution. Electrogram signal frequency is the frequency of thevariation of the net electric field potential at a recording electrode,as opposed to the frequency of the variation of tissue current.

An electrode is an electrical conductor. In accordance with someembodiments of the present invention, one or more electrodes aredesigned to be positioned in a patient's heart. The types of electrodesused in some embodiments of the present invention may be microelectrodesand may include, but are not limited to, solid conductors, such as discsand needles. In accordance with further embodiments of the presentinvention, the one or more electrodes are deployed in proximity tocardiac tissue using one or more catheters, which may be inserted viathoracotomy at the time of surgery, percutaneously, and/ortransvenously. Catheters and electrode configurations according to someembodiments of the present invention are discussed in detail below.

An electric field potential recorded by an electrode is the electricpotential energy o at the electrode location. The net electric fieldpotential recorded by an electrode is the sum of electric potentialsfrom different sources at the electrode location. With the uncommonexception of a single current source (as opposed to multiple spatiallydistributed current sources), a complex relationship exists between thenet electric field potential at a tissue site and the possible currentsource distributions that produced that net electric field potential.While a net electric field potential at any tissue site surrounded bymultiple spatially distributed current sources can be uniquelydetermined, the actual current source distribution that generated thenet electric field potential at a recording electrode cannot be uniquelydetermined. Thus, the use of electrogram recordings to reconstructtissue electrical events (e.g., local tissue activation frequency) maynot always provide an accurate prediction of circuit core density anddistribution. However, an electrogram signal frequency map of a tissuesubstrate that identifies changes in electrogram signal frequency may beoptimized to enhance the effectiveness and efficiency of ablationtreatments as described below in accordance with some embodiments of thepresent invention.

Electrode Spatial Resolution and Determination of Tissue SpatiotemporalVariation

Fractionated electrograms may be used as targets for ablation in atrialand ventricular arrhythmias. Fractionation has been demonstrated toresult when there is repetitive or asynchronous activation of separategroups of cells within the recording region of a mapping electrode.

In a study of temporal variation (i.e., spatially coordinated changes inthe frequency of activation) and spatiotemporal variability (i.e.,asymmetrical excitation of various tissue sites in time), tissueactivation patterns with increasing spatiotemporal variation weregenerated using a computer model. Virtual electograms were calculatedfrom electrodes with decreasing resolution. Then, electrogramfractionation was quantified. In addition, unipolar electrograms wererecorded during atrial fibrillation in 20 patients undergoing ablation.The unipolar electrograms were used to construct bipolar electrogramswith increasing inter-electrode spacing and quantified fractionation.During modeling of spatiotemporal variation, fractionation varieddirectly with electrode length, diameter, height, and inter-electrodespacing. When resolution was held constant, fractionation increased withincreasing spatiotemporal variation. In the absence of spatialvariation, fractionation was independent of resolution and proportionalto excitation frequency. In patients with atrial fibrillation,fractionation increased as inter-electrode spacing increased.

A model was developed for distinguishing the roles of spatial andtemporal electric variation and electrode resolution in producingelectrogram fractionation. Spatial resolution affects fractionationattributable to spatiotemporal variation but not temporal variationalone. Electrogram fractionation was directly proportional tospatiotemporal variation and inversely proportional to spatialresolution. Spatial resolution limits the ability to distinguishhighfrequency excitation from overcounting. In patients with atrialfibrillation, complex fractionated atrial electrogram detection varieswith spatial resolution. Electrode resolution must therefore beconsidered when interpreting and comparing studies of fractionation.Fractionated electrograms have attracted the attention of clinicalelectrophysiologists in the setting of mapping reentrant rhythms (eg,ventricular and atrial tachycardia) and more recently mapping of atrialfibrillation. Fractionation in these settings is felt to identifysubstrate relevant to the arrhythmia circuitry. Although fractionationcan identify a critical isthmus in scar-based reentrant ventriculartachycardia circuits, the use of fractionated electrograms to guideatrial fibrillation ablation has had conflicting results.

Although there is no uniformly accepted definition, the term “complexfractionated atrial electrograms” has been used to describe electrogramswith low amplitude and highfrequency deflections. Electrograms measurethe changing potential field at the site of a recording electrode. Anypattern of tissue activation within the recording region of an electrodethat results in alternation between increasing and decreasing potentialwill produce electrogram fractionation. Several disparate tissueactivation patterns have been shown to result in electrogramfractionation, including meandering rotors, wave collision,discontinuous conduction, and longitudinal dissociation. Because oftheir non-unique relationship (activation and electrogram), one cannotunambiguously determine a specific tissue activation pattern basedsolely on the observation of fractionation. Because fractionationresults from tissue dyssynchrony within the electrode recording region,it follows that the area of tissue that contributes to the electrogramwill influence fractionation. Spatial resolution refers to the area oftissue that contributes to the electrogram. Because tissue currentscreate a potential field that spreads infinitely through space, the“area that contributes to the electrogram” is in fact infinite.

However, because potential decreases with distance from a currentsource, the effective area that contributes to an electrogram is smalland varies with electrode size (length and diameter), configuration(unipolar versus bipolar), height above the tissue, and inter-electrodespacing. In a series of studies using a computer model of excitabletissue and electrogram recordings from patients with atrialfibrillation, the components that produce electrogram fractionation weredefined.

Activation was examined in a two-dimensional sheet of electricallyexcitable tissue using a computer model. The surrounding potential fieldproduced by tissue excitation was calculated. The model was used toindependently vary the temporal and spatiotemporal complexity of tissueexcitation. By recording from virtual electrodes of varied size,configuration, and height, the impact of spatial resolution onfractionation was quantified.

The model was a monodomain cellular automaton, in which the cells arearranged in a two-dimensional grid with each cell connected to its fourneighbors (up, down, left, and right). Cell voltage changes in responseto an action potential, external stimulation, or intercellular currentflow. The membrane voltage of a cell corresponds to its level ofelectrical depolarization. The resting state of a cell corresponds toquiescence. As a cell gathers current, membrane voltage depolarizes;when membrane voltage exceeds voltage threshold, an action potential isinitiated. Action potential upstroke velocity and action potentialduration are rate- and voltage-dependent. Cells connect to theirimmediate neighbors through electrically resistive pathways. Thevertical and horizontal resistive constants are Rv and Rh, respectively.Cells exchange current with their neighbors according to first-orderkinetics, whereby the voltage of a quiescent cell (j, k) at time t isaffected by that of its neighbors according to the following equation:

$\begin{matrix}{\frac{{dV}\left( {j,k,t} \right)}{dt} = {{\frac{1}{R_{h}}\left\lbrack {{V\left( {{j - 1},k,t} \right)} + {V\left( {{j + 1},k,t} \right)} - {2{V\left( {j,k,t} \right)}}} \right\rbrack} + {\frac{1}{R_{v}}\left\lbrack {{V\left( {j,{k - 1},t} \right)} + {V\left( {j,{k + 1},t} \right)} - {2{V\left( {j,k,t} \right)}}} \right\rbrack}}} & (9)\end{matrix}$

At each time step in the simulation, all cells have their values ofmembrane voltage updated according to the following equation:

$\begin{matrix}{{V\left( {j,k,t} \right)} = {{V\left( {j,k,{t - 1}} \right)} + {\frac{{dV}\left( {j,k,t} \right)}{dt}\delta\; t} + {Vintrinsic}}} & (10)\end{matrix}$where t is the time step size. A cell may be defined as scar, in whichcase it is permanently quiescent and electrically isolated from itsneighbors.

In a flat square sheet of tissue 1 cell thick (1010 mm) withoutanisotropy, temporal variation was introduced by modulating excitationfrequency. Activation wavefronts propagate through the homogeneoustissue at constant conduction velocity. Spatial variation was created byadding parallel lines of scar alternately extending to the top or bottomedge of the tissue. Spatiotemporal variation was then introduced bystimulating in the upper left corner; activation waves proceed throughthe tissue with a “zig-zag” pattern. Two components of tissue activationcomplexity could then be independently manipulated: (1) temporalvariation can be modulated by changing activation frequency; and (2)spatiotemporal complexity can be increased by increasing the number ofparallel lines of scar, that is, increasing the number of separatetissue bundles through which excitation spreads.

FIGS. 19A-19F illustrate temporal, spatial, and spatiotemporal variationof tissue excitation in accordance with some aspects of presentinvention. FIGS. 19A-19C illustrate tissue voltage distribution (singletime step; 1010 mm). FIG. 19A illustrates temporal variation, in whichstimulation of the top row of cells (cycle length 150 ms) producedsequential planar waves of excitation. FIG. 19B illustrates spatialvariation. Although tissue is divided by multiple alternating linearscars 190 and 192, activation proceeds from top to bottom in parallel(secondary to simultaneous stimulation of the top row of cells). FIG.19C illustrates spatiotemporal variation. Stimulation from the top leftcorner of the tissue results in sequential excitation of verticalchannels between linear scars 194 and 196, producing “zig-zag”activation waves every 150 ms.

FIGS. 19D-19F are corresponding virtual unipolar electrograms (electrodediameter 1 mm, height 0.5 mm, length 6 mm, and horizontal orientation)in accordance with aspects of the present invention. Note that even withlinear scars, if activation occurs simultaneously in all bundles, theelectrogram is very similar to that seen with in tissue without scars.To visualize this, compare FIGS. 19D and 19E. The contributions of eachbundle to the potential field occur simultaneously and are hencesuperimposed in the electrogram (no fractionation).

The potential Φ(m, n, t) was calculated that would be recorded by anelectrode placed at a height h above a site in the tissue plane (m, n)at each time (t). In the context of the monodomain approximation used,each cell in the tissue makes a contribution to the electrogram that isproportional to the cell's transmembrane current and inverselyproportional to its linear distance from the electrode. Thetransmembrane current at a particular cell was defined as the timederivative of voltage (V), approximated as the difference in V betweensuccessive time steps:

$\begin{matrix}{{\Phi\left( {m,n,t} \right)} = {\sum\limits_{j = 1}^{n}{\sum\limits_{k = 1}^{n}\frac{{V\left( {j,k,t} \right)} - {V\left( {j,k,{t - 1}} \right)}}{\sqrt{\left( {j - m} \right)^{2} + \left( {k - n} \right)^{2} + h^{2}}}}}} & (11)\end{matrix}$where j and k are position indices in the x and y directions.

FIG. 20 illustrates electrode geometry, spacing, and position accordingto some aspects of the study and the present invention. In the study,three-dimensional cylindrical electrodes 200 with varied length 202,diameter 204, and height 206 were modeled. The electrodes were modeledas hollow cylinders divided into a finite element mesh with elementsevenly distributed about the circumference and along the length 202 ofthe electrode. The number of elements varied depending on electrodegeometry so no element area was 1 mm². The electric potentialcontribution from each cell was calculated at the center of eachelement. The potential recorded by the entire unipolar electrode wasthen calculated as the sum of each element potential multiplied by theelement area and divided by the total surface area of the electrode.

The bipolar electrogram was obtained simply as the difference in thepotentials recorded by the two unipolar electrodes. Height 206 wasmeasured from the tissue to the electrode's bottom edge and, for bipolarrecording, inter-electrode spacing 208 was measured between edges.Electrodes were positioned over the center of the tissue (perpendicularto lines of scar—unipolar; parallel to lines of scar—bipolarrecordings). Electrode spatial resolution varies inversely withelectrode surface area (length and diameter), height above tissue, andinter-electrode spacing (for bipolar recordings).

The cellular automaton model evolved through discrete time steps; as aresult, electrogram amplitude fluctuated from time step to time step.The electrogram signal was therefore processed with a smoothing functionto reduce this artifact. The number of turning points was quantified asthe number of peaks and troughs with a 10% tolerance.

Two 60-second unipolar recordings were obtained during atrialfibrillation from the coronary sinus of 20 patients presenting foratrial fibrillation ablation. Unipolar electrograms (indifferentelectrode in the inferior vena cava (length=diameter=2 mm; availablefrom Bard Electrophysiology (Billerica, Mass.)) were recorded witheither a 20-pole (1-mm electrodes, 1-3-1-mm spacing; 10 patients) or a10-pole (2-mm electrodes, 2-5-2-mm spacing; 10 patients) catheter(available from Biosense Webster (Diamond Bar, Calif.)). Signals(sampled at 1 kHz, filtered 30-250 Hz) were exported for offlineanalysis. From these we constructed bipolar electrograms with increasinginter-electrode spacing (electrodes 1-2, 1-3, and 1-4). Bipolar signalswere analyzed using standard algorithms for average interpotentialinterval (AIPI) and interval confidence level (ICL). The voltage windowfor ICL was 0.05 to 0.2 mV; the upper limit of 0.2 mV was selected as anaverage of values used by different groups. The amplitude ofelectromagnetic noise in each signal was measured in 10 patients (duringsinus rhythm).

A mixed effects linear model was used for the analysis of theexperimental data for studying fractionation as a function ofinter-electrode spacing. Data for each catheter type and each outcome(ICL and AIPI) were analyzed separately. Subjects within a catheter typewere treated as random effects, thereby inducing a compound-symmetricalcorrelation structure among withinsubject measurements. Measurementsbetween subjects were independent. inter-electrode spacing and time ofmeasurement were treated as fixed effects with time of measurementnested within subject. Analysis was done using PROC MIXED in SAS,Version 9.3.

Results showed that fractionation is a function of temporal variation.In a series of simulations tissue (without linear scars) was stimulatedat progressively shorter cycle lengths (150, 125, 100, and 75 ms).Virtual electrograms were recorded using unipolar electrodes (6-mmlength, 1-mm diameter, and 0.5-mm height). Fractionation was directlyproportional to tissue frequency; 15, 24, 38, and 93 deflections atcycle lengths of 150, 125, 100, and 75 ms, respectively. FIG. 21A is agraph illustrating fractionation as a function temporal variation by thenumber of deflections versus stimulus cycle length according to someaspects of the study and the present invention. The underlying datacorresponds to electrode length 2, 4, 6, and 8 mm (with fixed diameter 1mm, height 0.5 mm). FIG. 21B is a series of virtual unipolarelectrograms from tissue excited at decreasing cycle lengths: cyclelength 150 ms (top) to 75 ms (bottom), recorded with a unipolarelectrode of 2 mm (left) and 8 mm (right) in length. The number ofdeflections is independent of electrode size.

Results showed the impact of electrode spatial resolution in tissue withtemporal variation on fractionation. With temporal variation alone,fractionation was independent of electrode spatial resolution, as shownin FIGS. 21A-21B, in accordance with some embodiments of the presentinvention. In tissue without scars stimulated at 150-ms cycle length,the number of deflections in the unipolar electrogram was independent ofelectrode length, diameter, or height (15 deflections for electrodelength 2, 4, 6, and 8 mm; diameter 1, 2, 3, and 4 mm; height 0.5, 1, 2,and 3 mm). Bipolar recordings (1-mm length and diameter, 0.5-mm height)had 27 deflections regardless of inter-electrode spacing (1, 3, 5, and 7mm).

Results showed that fractionation is a function spatiotemporalvariation. To create spatiotemporal variation, tissue was stimulated ata fixed cycle length of 150 ms from the upper left corner resulting in a“zig-zag” activation pattern. When electrode spatial resolution was keptconstant, fractionation was directly proportional to the number oflinear scars (i.e., spatiotemporal complexity); the number ofdeflections was 19, 26, 45, and 52 for tissue with 1, 2, 4, and 6 linesof scar, respectively (unipolar 6-mm length, 1-mm diameter, and 0.5-mmheight). With bipolar recordings (1-mm length and diameter, 0.5-mmheight, and 5-mm inter-electrode spacing), there were 24, 25, 29, and 32deflections for tissue with 1, 2, 4, and 6 lines of scar, respectively.

FIG. 22A is a graph of number of deflections in unipolar recordings as afunction of spatiotemporal variation (number of scars) and electroderesolution (length; diameter 1 mm, height 0.5 mm). FIG. 22B is a seriesof virtual electrograms from tissue stimulated every 150 ms withincreasing spatiotemporal variation (1 scar [top] to 6 scars [bottom])recorded with a unipolar electrode (length 2 mm [left] and 8 mm[right]). The number of deflections increases with decreased electroderesolution (and the effect is more prominent as the number of scarsincreases).

Results showed the impact of electrode spatial resolution in tissue withspatiotemporal variation on fractionation. In the setting ofspatiotemporal variation (cycle length 150 ms, varied number of scars),the number of turning points increased in proportion to unipolar length(diameter 1 mm and height 0.5 mm) and number of linear scars. In tissuewith 6 lines of scar, the number of deflections was proportional toelectrode diameter: 52, 66, 74, and 76 deflections for electrodes of 1-,2-, 3-, and 4-mm diameter, respectively (length 6 mm and height 1 mm).With constant electrode size (length 6 mm and diameter 1 mm), the numberof deflections was directly proportional to electrode height: 52, 68,76, and 84 deflections at heights of 0.5, 1, 2, and 3 mm above thetissue, respectively. Fractionation also increased with increasinginter-electrode spacing: 22, 24, 32, and 33 deflections forinter-electrode spacing 1, 3, 5, and 7 mm, respectively (1-mm length anddiameter, 0.5-mm height).

Qualitatively the effect of inter-electrode spacing on spatialresolution (in sinus rhythm) and fractionation (during atrialfibrillation) is easily appreciated. FIG. 23A is a fluoroscopic image of10-pole catheter 230 in the coronary sinus (electrode length 2 mm,inter-electrode spacing 2-5-2 mm). Brackets indicate inter-electrodespacings used for reconstruction of bipolar recordings. FIG. 23B isafluoroscopic image of 20-pole catheter 232 (electrode length 1 mm,inter-electrode spacing 1-3-1 mm). FIG. 23C is a set of simultaneouselectrogram recordings during sinus rhythm and atrial fibrillation withinter-electrode spacing of 1, 5, and 7 mm. There is a minor increase inbaseline noise as inter-electrode spacing increases (sinus rhythm) andincreased fractionation with increased inter-electrode spacing (atrialfibrillation).

To quantify the effects of spatial resolution on complex fractionatedatrial electrogram, we measured ICL and AIPI as a function ofinter-electrode spacing during atrial fibrillation. Fractionationincreased with increasing inter-electrode spacing. Average values (andSEs) were as follows: ICL 10-pole catheter: 5.2±1.0, 8.7±1.0, and9.5±1.0 for 2, 9, and 13 mm inter-electrode spacing, respectively(P<0.001, 2 versus 9 and 2 versus 13 mm); 20-pole catheter: AIPIconfidence level 6.8±1.0, 9.9±1.0, and 10.3±1.0 for 1, 5, and 7 mminter-electrode spacing, respectively (P<0.001, 1 versus 5 mm and 1versus 7 mm). AIPI decreased with increased inter-electrodespacing—10-pole catheter: 207±19, 116±19, and 106±19 for 2, 9, and 13 mminter-electrode spacing, respectively (P<0.001, 2 versus 9 mm and 2versus 13 mm); AIPI 20-pole catheter: 144±13, 99±13, and 92±13 (P<0.001,1 versus 5 mm and 1 versus 7 mm). As inter-electrode spacing increases,electrodes record signals from locations that are progressively fartherapart and are therefore exposed to different electromagnetic noise.Bipolar recordings reflect only the difference between the signalsrecorded at each electrode; therefore, as the difference in noiserecorded at each electrode becomes greater, the amplitude of noise inthe bipolar signal becomes larger. As a result one can expect that noiseis progressively increased as inter-electrode spacing increases. Noisewas measured as a function of inter-electrode spacing; the meanamplitude of noise increased with inter-electrode spacing but remained0.05 mV (maximum 0.028 0.01 mV).

The fact that electrodes measure electric potential rather than tissuecurrent density creates a possible source of ambiguity in theinterpretation of electrograms. Because currents generate a potentialfield that spreads through space (with amplitude that decreases withdistance), potential recordings at any site reflect contributions fromcurrent sources at multiple sites. This capacity for “far-field”recording has the result that electrogram deflections occur withvariation of current density over an area larger than the physicaldimensions of the electrode. Electrogram fractionation is generallydefined as low-amplitude, high-frequency deflections. As the number ofsites contributing to an electrode's potential increases, the number ofdeflections will increase so long as these sites are excitedasynchronously. When sites are excited simultaneously, their impact onthe electrogram amplitude is additive but fractionation does not result.

In the study, a simple model was used to independently control each ofthe components that contribute to fractionation: tissue spatiotemporalvariation, tissue temporal variation, and electrode spatial resolution.The following observations were made: (1) fractionation is not observedwith spatial variation alone; secondary to temporal superposition, thecontributions from spatially disparate currents to the potentialrecorded at any electrode location sum to alter amplitude withoutproducing fractionation; (2) fractionation is observed with temporalvariation, which is independent of electrode spatial resolution; and (3)fractionation is observed with spatiotemporal variation and in this caseis dependent on electrode spatial resolution. Consequently, spatialresolution determines the limit of the ability to distinguish temporalfrom spatiotemporal variation; that is, increased frequency as a resultof overcounting.

Electrogram fractionation results from the interaction of 3 components:tissue temporal variation, tissue spatiotemporal variation, andelectrode spatial resolution. In the absence of tissue spatiotemporalvariation (ie, temporal variation alone), fractionation is independentof electrode spatial resolution. In a computer model of electricallyexcitable tissue with spatiotemporal variation and in patients withatrial fibrillation, fractionation increased with decreasing electrodespatial resolution. Electrograms measure the average potential field atthe surface of an electrode over time. As a consequence, multipledifferent patterns of tissue activation can generate similarelectrograms. Analysis of a single fractionated electrogram does notpermit differentiation of temporal versus spatiotemporal tissuevariation; therefore, one cannot distinguish highfrequency excitationfrom overcounting. Electrode spatial resolution must be considered whencomparing studies of fractionation.

In another study, a computational model of an electrode situated above asheet of excitable tissue, validated against experimental measurementsin vitro, was used to determine how spatial resolution is affected byelectrode diameter, electrode length, inter-electrode distance (in thecase of bipolar recordings), and height of the electrode above a dipolecurrent source, and how spatial resolution could be varied overclinically relevant ranges.

Mapping during atrial fibrillation frequently reveals fractionatedelectrograms that confound identification of local activation time andtherefore preclude activation mapping. Optimizing electrodeconfiguration and placement to minimize the area of tissue seen by theelectrode is thus crucial to accurate activation mapping of atrialactivity, which in turn may facilitate successful ablation of atrialfibrillation.

Using a custom software (MATLAB®, available from The Mathworks Inc.,(Natick, Mass.)), the potential field surrounding a dipole currentsource was modeled to represent the basic unit of electric potentialgeneration from heart tissue, namely, a flow of current from theinterior of a cell to the extracellular space as the cell depolarizesand an equal and opposite currently flow nearby as adjacent cellsrepolarize. The potentials were calculated as would be recorded byelectrodes of various diameters d and lengths l placed relative to thisdipole source at various positions along the y-axis and at variousheights z₀ when the positive and negative current sources were placed aty=±δ/2. The electrodes for bipolar electrode recordings, were separatedby a nearest surface distance of Δ. FIG. 24 is a schematic of a dipolecurrent source located at ±δ/2 about the origin and a bipolar pair ofelectrodes of diameter d and height l separated by Δ and located atheight z₀ along the y-axis.

Arbitrary units were assigned to δ=0.25 mm and ρ=1. The electrodes weremodeled as hollow cylinders divided into a finite element mesh with 30elements evenly distributed about the circumference and 15 elementsalong the length for a total of 450 elements of equal area. The electricpotential produced by the dipole source was calculated at the center ofeach element. The potential recorded by the entire unipolar electrodewas then calculated as the sum of each element potential multiplied bythe element area and divided by the total surface area of the electrode.The bipolar electrogram was obtained simply as the difference in thepotentials recorded by two unipolar electrodes.

An in-vitro apparatus was created for confirming that commonly usedclinical intracardiac electrodes do, in fact, record potentials as ourmodel predicts. A Plexiglas chamber was filled with 0.9% saline. Two0.3-mm wide copper wires with flat ends were fixed 0.5-mm apart (centerto center) into the bath (the x-y plane shown in FIG. 24) with onlytheir tips exposed to the bath interior. Biphasic square wave impulses(2.4 mV, 10-ms pulse width) were delivered to the electrodes to simulatea dipole source in the heart tissue. Recording electrodes (both unipolarand bipolar) were also placed in the saline bath and positioned with amicromanipulator attached to a machined aluminum base under the bath.The electrode positions could be adjusted with a resolution of ±0.1 mmover 10 cm.

Unipolar electrode recordings were taken with standard catheters(available from Biosense Webster Inc. (Diamond Bar, Calif., USA)) havingelectrode tips of width 2.333 mm and lengths of 1, 4, and 8 mm. Bipolarrecordings were taken between the tip electrodes on two standardcatheters (Biosense Webster Inc.) having a variety of inter-electrodespacing (1, 2, 3, 4 mm). The recording electrodes were oriented to beperpendicular to the bath floor at a height of 1 mm, as diagrammed inFIG. 24.

The electrograms from the recording electrodes were sampled at 1 kHz andfiltered from 0.5 to 250 Hz (available from Bard EP (Lowell, Mass.)).Ten recordings were taken using each electrode configuration at 10positions along the y-axis at intervals of 0.2 mm. The entire set ofrecordings was repeated five times, with the order of catheter positionsreversed (and electrodes polished) between runs to minimize effects dueto electroplating of the cathode. Signals were exported and analyzedoffline with the use of MATLAB®-based software.

FIGS. 25A-25B are unipolar and bipolar space domain electrogramscalculated with the computational model and measured in the physicalin-vitro model. Unipolar electrodes with tips having lengths of 1, 4,and 8 mm (2.33-mm diameter) were examined, and correlation coefficientswere found of 0.99, 0.99, and 0.97, respectively, between the computedand measured electrograms. Bipolar recordings with inter-electrodespacings of 1, 2, 3, and 4 mm (2.33-mm tip diameter) were examined, andcorrelation coefficients of 0.99 were found in all cases.

Two measures of spatial resolution were used. The first is theconventional distance to half amplitude used to quantify the spread ofmany measurement functions. The space domain electrograms for unipolarand bipolar electrodes have more than a single peak, as shown in FIGS.25A-25B, but the distance to half amplitude concept still usefullyapplies. Thus, the resolution provided by a unipolar recording of adipole source was equated to the lateral distance from the dipole centerto the point of half maximal amplitude, defined as W_(1/2), which forbipolar recordings was taken as the distance from its center to thepoint of half maximum positive deflection. FIG. 26A is a plot of thepotential due to a dipole current source recorded by a unipolarelectrode as a function of lateral distance from the source, showing howresolution is quantified in terms of peak width at half maximum heightW_(1/2). FIG. 26B is the corresponding plot for a bipolar electrode.

Due to concern that the two and three peaks, respectively, of theunipolar and bipolar point-source electrograms might make the resolutionof multiple sources more complicated than if they had only single peaks,a second measure of spatial resolution was designed to detect theminimal resolvable separation between two dipole sources. Consideringresolution in the y direction, Φ₀(y,z₀) was defined as the electrogrammeasured when the dipole sources are separated by a distance of zero(i.e. equivalent to a single dipole source), and Φ_(Δy)(y,z₀) wasdefined as the electrogram measured when the sources are separated bysome finite distance Δy.

When Δy is small compared with d, Φ₀(y,z₀) and Φ_(Δy)(y,z₀) are similar.Consequently, their cross correlation achieves a maximum value close to1, becoming precisely 1 in the limit as Δy approaches zero. When Δy issufficiently large, Φ_(Δy)(y,z₀) assumes the appearance of two distinctdipole electrograms located at well separated positions, so the crosscorrelation between Φ₀(y,z₀) and Φ_(Δy)(y,z₀) again achieves arelatively high maximum value. At intermediate separations, Φ_(Δy)(y,z₀)consists of two partially overlapping dipole electrograms and thus has acomplex morphology that bears little resemblance to that of a singledipole. In this case, the cross correlation between Φ₀(y,z₀) andΦ_(Δy)(y,z₀) has a relatively low maximum value because the two signalsare dissimilar in shape. Thus, the nominal measure of resolution wasselected to be the value of Δy for which the maximum in the crosscorrelation between Φ₀(y,z₀) and Φ_(Δy)(y,z₀) achieves its minimumvalue. This is defined as C_(min).

FIG. 27A is a plot of superimposed simulated bipolar electrograms (d=2mm, 1=z=Δ=1 mm) produced by two dipole sources with Δy=0, 0.5, 2.95, and3.5 mm (as indicated in the legend). FIG. 27B is a plot of the maximumon the cross correlation between the bipolar electrogram with Δy=0 andthe electrogram with Δy as indicated on the horizontal axis. Opencircles correspond to the four electrograms shown in FIG. 27A. Thisrelationship has a maximum for Δy=0 mm and a minimum for Δy=3.9mm=C_(min).

FIGS. 28A-28C are plots illustrating how the two measures of spatialresolution, W_(1/2) (dotted lines) and C_(min) (dashed lines), vary asfunctions of electrode dimensions when the potential from a dipolecurrent source is recorded by a unipolar electrode. The nominal baselinevalues for the various quantities in question were set as d=2 mm, 1=1mm, and z₀=1 mm, and each quantity was varied in turn while the othersremained fixed. Not surprisingly, the two measures of resolution are notprecisely equal. Nevertheless, they are clearly comparable and exhibitsimilar trends, both showing that resolution worsens progressively as d,l, and z₀ increase. It is also clear that resolution depends moststrongly on z. FIGS. 28A-28C: Resolution of a unipolar electroderecording of a dipole current source as assessed in terms of C_(min)(solid lines) and W1/2 (dashed lines). The three plots show dependenceof resolution on electrode diameter (d), length (l), and height abovethe tissue (z0). Although each of these quantities was varied, theremaining quantities were held fixed at d=2 mm, 1=1 mm, and z0=1 mm.FIG. 29A-29D are corresponding plots for bipolar electrode recordings,including showing the effects of changing the distance D between the twoelectrodes of a bipolar pair (FIG. 1). In deciding what conditionscorrespond to the highest electrogram accuracy that is currentlyachievable, the fact that the myocardial tissue is covered with a layerof endothelial cells that adds to the distance between the active tissueand the closet approach of an electrode tip. Thus, even when anelectrode is placed right against the tissue surface, a nominal bestcase scenario would place it an average of approximately 1 mm from theactive tissue. Currently, the smallest clinically available electrodeshave diameter and length both of 1 mm. Setting these conditions in ourcomputational model (i.e. z0=d=1=1 mm), resolution values were obtainedfor a unipolar recording of Cmin=4.5 mm and W1/2=3.0 mm. For a bipolarrecording (imposing the additional condition that D=1 mm), Cmin=2.8 andW1/2=4.0 mm were obtained. Reducing d to the relatively negligible valueof 0.001 mm while keeping the remaining parameters unchanged, reducedW1/2 and Cmin by factors of between 2 and 4. Conversely, reducing 1 to0.001 mm, reduced W1/2 and Cmin by factors of between 1.6 and 2.9. Thus,by reducing an electrode to a single point one would improve resolutionover that currently achievable by the product of these two effects, orroughly one order of magnitude.

Identification of atrial activation patterns depends crucially on theability to create spatially accurate maps of atrial electrical activity.The fact that this activity is often complex and nonperiodic would makemapping a significant challenge even if the entire activity patterncould be visualized perfectly. In reality, the practicing cardiacelectrophysiologist must make do with nothing more than a series ofelectrograms from a small number of electrodes placed on the atrialendocardium. The challenge of mapping is further compounded becausethese electrograms are distance-weighted averages of the activity froman extended region of heart tissue in the vicinity of each electrode. Inparticular, when different patches of tissue each provide out of phasecontributions to the potential measured by a single electrode, theresult is a fractionated electrogram. Consequently, it is most desirableto obtain electrograms of the highest achievable spatial resolution.Resolution of a bipolar electrode recording of a dipole current sourceas assessed in terms of Cmin (solid lines) and W1/2 (dashed lines). Thefour plots show dependence of resolution on electrode diameter (d),length (l), separation (D), and height above the tissue (z0). Althougheach of these quantities was varied, the remaining quantities were heldfixed at d=2 mm, 1=1 mm, D=1 mm, and z0=1 mm. Here, two differentmeasures of resolution (FIGS. 26A-26B) were used to investigate howspatial resolution is affected by the dimensions and configuration ofboth unipolar (FIGS. 28A-28C) FIGS. 29A-29D: Resolution of a bipolarelectrode recording of a dipole current source as assessed in terms ofCmin (solid lines) and W1/2 (dashed lines). The four plots showdependence of resolution on electrode diameter (d), length (l),separation (D), and height above the tissue (z0). Although each of thesequantities was varied, the remaining quantities were held fixed at d=2mm, 1=1 mm, D=1 mm, and z0=1 mm. and bipolar (FIGS. 29A-29D)electrograms. The resolution degrades progressively and substantially aselectrode width, height, separation (in the case of bipolar), anddistance from the tissue are increased. Changes in electrode height hadthe greatest impact on spatial resolution, however, implying that themost important aspect of electrode design is not related to theelectrode itself, but rather to the physical proximity of the electrodeto the tissue. There are two principle ways in which the spatialresolution of intracardiac electrode recordings can be diminished: theamount of tissue that is ‘near field’ [i.e. immediately beneath theelectrode(s)] can be increased, and/or the ratio of near-field tofar-field tissue can be diminished. An increased electrode diameterresults in an effective increase of the electrode's footprint over themyocardial surface, thereby increasing the amount of tissue contributingto the near-field signal. In contrast, an increased electrode heightresults in greater attenuation of near-field signal relative tofar-field signal, resulting in a diminished ability to discriminatebetween the two. An increased electrode length has a similar effectbecause it also increases the average height of the electrode above thetissue surface. These various effects are experienced by both unipolarand bipolar electrodes (FIGS. 28A-28C and 29A-29D), although to a lesserextent by bipolar because taking the difference between two nearbypotentials effectively cancels the common far-field components whilespatially differentiating the near-field signal. The theory ofintracardiac electrode measurement performance has been known for manyyears. For example, in 1951 Schaefer et al. [10] outlined themathematical relationship describing how unipolar and bipolarelectrograms are affected by the distance between a dipole source andthe recording electrode(s), and observed that bipolar electrodes reducedfar-field ‘contamination’ and that this effect was increased asinter-electrode spacing was decreased. Later in the same decade, Durreret al. [11] investigated methods for measuring electrical activation inthe canine left ventricle and made the qualitative observation that onlywith bipolar recordings ‘y Can the influence of activity in distantparts of the heart be excluded’. They also described unipolar andbipolar electrogram morphologies corresponding closely to thosesimulated in the present study (FIGS. 25A-25B), and noted thatincreasing the spacing between bipolar electrodes caused the electrogrammorphology to change in the same way as our model simulations predict(FIGS. 27A-27B). Similar investigations have been undertaken morerecently by other investigators [12,13] and corroborate our findingswith respect to unipolar and bipolar electrogram morphologic features.The notion that various electrode characteristics should affect spatialresolution is also not new. For example, Kimber et al. assessed theability of unipolar and bipolar recordings to accurately determine localactivation time in ‘ambiguous’ or fractionated signals from ventriculartachycardia mapping studies and found that bipolar recordings werebetter able to determine local activation time. Nevertheless, to ourknowledge, there has been no formal study quantifying how electrodecharacteristics affect the spatial resolution of intracardiacelectrograms, despite the important implications for clinicalelectrophysiology. The foundation of activation mapping isidentification of local activation time, which is dependent on spatialresolution [14]. During organized rhythms, the resolution provided bycurrently available electrodes is adequate for accurately identifyinglocal activation times. However, this is not always the case for atrialfibrillation in which tissue activation can have high spatiotemporalcomplexity, changing rapidly with time [15]. This would lead tomeaningless maps if local activation time is sampled sequentially with asingle mapping electrode. It would thus appear that accurate mapping ofatrial fibrillation will require the use of electrode arrays to providebeat-to-beat activation at multiple sites simultaneously. This raisesquestions as to the ideal size and spacing of electrodes in the array.Our results indicate that with the smallest electrodes currentlyavailable, one cannot expect a resolution of better than about 5 mm(FIGS. 28A-28C and 29A-29D), therefore spacing the electrodes any closerthan this is unlikely to confer added benefit unless methods of digitalsignal processing such as deconvolution can be used to further enhanceresolution.

A computational model was created and validated for evaluating theimpact of electrode size, shape, inter-electrode spacing, and heightabove the tissue on spatial resolution. Two independent metrics wereused to quantify spatial resolution, both indicating that spatialresolution becomes degraded roughly in proportion to the above fourfactors. Electrode height above the tissue has the greatest effect onspatial resolution, so electrode tissue contact is the most importantfactor impacting resolution. Finally, these calculations suggest thateven if electrodes could be constructed to have negligible dimensionscompared with those in use today would increase resolution by at mostabout one order of magnitude. Increases in all these quantities causedprogressive degradation in two independent measures of spatialresolution, with the strongest effect being due to changes in heightabove the tissue.

The accuracy of any electrogram signal frequency analysis is a functionof the ratio between electrode spatial resolution and tissuespatiotemporal variation. The voltage (i.e., the electric potentialdifference) of an electrogram rises and falls with the net electricfield potential at the recording electrode, and the electrogram signalfrequency is simply a measure of the frequency of those variations involtage. Any factor that influences the voltage will also influence theelectrogram signal frequency. Because the magnitude of an electric fieldpotential decreases with radial distance from its current source, thenet electric field potential at a recording electrode will be dominatedby nearby current sources. Effectively, only a limited region of tissuein the vicinity of a recording electrode substantively contributes tothe net electric field potential recorded by that electrode. The spatialextent of such an electrode recording region is the spatial resolutionof that electrode.

Meanwhile, spatiotemporal variation (caused by, for example, heart cellswhose excitations are dissociated and hence out of phase from eachother) between current sources within an electrode recording region mayproduce a deflection in the electrogram recording. A deflection resultsin an electrogram signal frequency that is higher than the tissueactivation frequency of any individual cell within the electroderecording region. Thus, an attempt to determine the maximum tissueactivation frequency of individual cells may be inaccurate in thepresence of spatiotemporal variation within the electrode recordingregion.

The accuracy with which an electrogram signal frequency indicates thetissue activation frequency of individual cells within the recordingregion is a function of the ratio between the spatial resolution of therecording electrode and the spatiotemporal variation of the tissue. Oncethe electrode recording region is limited to only cells that aresynchronously excited, the electrogram signal frequency becomes the sameas the tissue activation frequency in the recording region. This“threshold” spatial resolution and/or higher spatial resolutionsaccurately reflect tissue activation frequency without over-counting.Therefore, the correlation between electrogram signal frequency andtissue activation frequency (and thus circuit density and distribution)increases as the spatial resolution of the recording electrode increases(i.e., includes fewer cells that are dssynchronously activated); and theoptimal spatial resolution is close to the threshold wheredssynchronously activated cells are eliminated.

The threshold spatial resolution is different for each patient (and atdifferent locations in each patient's heart). In accordance with someembodiments of the present invention, the threshold spatial resolutionmay be found by iteratively employing recording electrodes with higherspatial resolutions until dssynchronously activated cells are eliminatedfrom the recording region. As spatial resolution is increased,electrogram signal frequency will change if dyssynchrony remains withinthe recording region. The spatial resolution at which electrogram signalfrequency no longer changes (with improved spatial resolution) may beconsidered an accuracy-promoting spatial resolution threshold for aparticular recording region.

FIG. 13 is a system component diagram in accordance with someembodiments of a system for identifying an optimal spatial resolutionfor local tissue with spatiotemporal variation. The system may include,but is not limited to, an imaging subsystem 131 (described above) and/ora catheter subsystem 132. The system may also include a processing unit135, a memory 134, a transceiver 133 including one or more interfaces139, a GUI 138, and/or a display 136 (each described in detail below).

The catheter subsystem 132 includes one or more catheters according tosome embodiments of the present invention. In some embodiments, thecatheter subsystem 132 also may include, but is not limited to, one ormore puncture or surgical devices for accessing a patient's vasculatureand/or heart, one or more sheaths with one or more valves for preventingflowback, a saline solution for flushing components of the subsystem,one or more guidewires for positioning the one or more catheters, and/orone or more contrast agents (used in combination with an appropriateimaging subsystem 131) for viewing the tissue during use. The cathetersubsystem 132 may include a separate display and/or share a display 136with other components of the system shown in FIG. 13. The cathetersubsystem 132 and its components may be operated manually and/orautomatically.

According to some embodiments of the present invention, the cathetersubsystem 132 also may include, but is not limited to, one or moreelectrode localization technologies, such as triangulation-basedlocalization, radio-frequency-based localization (e.g., the CARTO™ XPSystem, which is available from Biosense Webster® (Diamond Bar,Calif.)), and/or impedance-based localization (e.g., the EnSite NavX™Navigation & Visualization Technology, which is available from St. JudeMedical (St. Paul, Minn.)).

FIG. 30 is a process flowchart for identifying an optimal spatialresolution for local tissue with spatiotemporal variation in accordancewith some embodiments of the present invention. In step 301, anelectrogram recording is acquired for a particular tissue location usingan electrode with an initial spatial resolution. In step 302, thefrequency of the electrogram signal is calculated and stored. In step303, another electrogram recording is acquired using an electrode with aspatial resolution that is higher than that of the previous electrode.In step 304, the frequency of the electrogram signal is calculated and,in step 305, compared to the frequency of the previous electrogramsignal. If the frequency has changed, the process returns to step 303using an electrode with a spatial resolution that is even higher yet. Insome embodiments, the frequency must change substantially to return tostep 303; while in other embodiments, any change in the frequencyrequires returning to step 303. If the frequency has not changed, thespatial resolution is identified in step 306 as a minimum threshold forand/or optimal spatial resolution. In some embodiments, the frequencymust not change at all to identify the optimal spatial resolution; whilein other embodiments, a small change in the frequency is not consideredin identifying the optimal spatial resolution.

Spatial resolution is influenced by electrode location, size, andconfiguration. More specifically, spatial resolution can be improved bythe following: (1) moving the electrode closer in proximity to thetissue surface (i.e., the current source); (2) reducing the size of theelectrode itself; and (3) using a bipolar electrode configuration (oranother means of producing spatial differentiation). The electrodeconfiguration is not limited to only two electrodes, but may includemore than two electrodes, and the differences between the electric fieldpotentials may still be calculated.

The distance between an electrode and the tissue as well as the size ofan electrode matter because an electrode is an electrical conductor thatcannot support a voltage gradient. Instead, an electrode records theaverage of all electric potentials on its surface. Thus, spatialresolution will be reduced to the extent that positioning and/or anincrease in electrode size results in an increase in the average heightof an electrode above the tissue. Likewise, spatial resolution will bereduced to the extent that an increase in electrode size results in anelectrode covering a larger region of tissue. Again, because anelectrode recording is an average of all electric potentials, a largerelectrode “footprint” eliminates the ability to distinguish between thecontributions to the field potential of individual heart cells withinthat footprint.

Practically, all electrode recordings are bipolar; but by convention, anelectrode configuration is “unipolar” when only one of twoelectrodes—the “index” electrode—is close enough to the tissue to recorda signal, while the second electrode—the “indifferent” electrode—is farenough from the tissue that it does not record a signal and/or cannot bein contact with the tissue. On the other end of the spectrum, when bothelectrodes may be in contact with the tissue to record a signal, anelectrode configuration is “contact bipolar.” FIGS. 31A and 31Billustrates an example of a contact bipolar electrode configuration.Catheter 313 has two electrodes 314, both of which are close enough totissue surface 315 to record a signal.

As an electric field potential spreads outward from a current source,its magnitude diminishes with the radial distance r from the source at arate of about 1/r² for unipolar electrogram recordings. For bipolarelectrogram recordings, the magnitude of an electric field potentialdiminishes more rapidly, at a rate of about 1/r³. The difference betweenthe electric potentials as recorded by two bipolar electrodes may berepresented by:

$\begin{matrix}{{\delta\;\psi} \propto {\frac{1}{r^{3}} - \frac{1}{\left( {r + d} \right)^{3}}}} & (12)\end{matrix}$where Ψ is the electric field potential and d is the distance betweenthe two bipolar electrodes. Both the magnitude of the electric fieldpotential at each electrode and the difference between the tworecordings decrease as the distance to the current source increases.Thus, when using a bipolar configuration, the potential differencebecomes negligible for potential current sources that are far from thetwo electrodes relative to the distance between those electrodes.Spatial resolution is higher if sources far from the recording site arenot contributing substantively to the electrogram. Hence, bipolarelectrogram recordings possess better spatial resolution than unipolarelectrogram recordings.OCU Electrode Configuration

For most current electrophysiological procedures, intracardiacelectrodes are used to measure electrical activity within the heart.There are generally two electrode types: unipolar and bipolarelectrodes. Unipolar electrodes are the simplest configuration, with onerecording electrode within the heart and another at a relatively longdistance away. Unipolar electrodes are adequate but have a tendency toinclude far field electrical activity in the recorded signal which canresult in a fractionated electrogram. This is a particularly relevantwhen trying to map complex arrhythmias (e.g. cardiac fibrillation) andaccurately identifying local activation time. Bipole electrodeconfigurations ameliorate this problem by placing both electrodes withinthe heart at a relatively narrow distance apart. Since both electodes“see” approximately the same far field electrical activity and therecorded potential is the difference of the two the resultantelectrogram includes little far field signal.

There are, however, at least two limitations of bipole electrodes.First, the recorded electrical potential of bipole electrodes vary withtheir orientation relative to the direction of a passing wavefront.Second, because bipole electrodes have both electodes on the heartsurface, there is potential inclusion of distinctly different electricalactivity from each electrode. In view of these limitations, it washypothesized that bipolar electrodes oriented perpendicular to thetissue plane (orthogonal close unipolar (OCU)) retain the superiornear/far-field discrimination of common bipolar electrode recordingswith the directional independence and smaller footprint of unipolarrecordings. A series of in silico and in vivo experiments were performedto test the potential utility of this hypothesis.

Electrical excitation was modeled as a static dipole with 0.5 mmspacing. The direction of the dipole moment is parallel to “wavedirection.” Electrodes were modeled as cylinders with the samedimensions as those used in the in vivo experiments (1-mm length, 2-mmdiameter, 4-mm spacing).

FIG. 32 illustrates the collection of electrograms in accordance withsome aspects of the study. Electrograms were recorded in a plane of aheight (1 mm) above the dipole moment using electrodes 320 with length(1 mm) diameter 324 (2 mm). To assess the effect of wavefront direction,electrode bipoles with inter-electrode distance 236 were orientedparallel, perpendicular, and orthogonal to the dipole moment.Measurements were made with the electrode bipoles directly over thedipole, and at increments (0.1 mm) up to a determined distance (10 mm)from the dipole in direction 327.

FIG. 33 illustrates the collection of electrograms in accordance withsome aspects of the study. Near field dipole is at the origin, and farfield dipole 1 mm along the x axis. Electrical potential is measured asthe electrodes move along the y axis. Common bipolar and OCUelectrograms were recorded from two dipoles to assess near- andfar-field discrimination. A first dipole was the near field signal, anda second dipole was the far field signal. Measurements were made withthe electrode bipoles directly over the first dipole, and at increments(0.1 mm) up to a determined distance (10 mm) from the second dipole indirection 327.

Electrical potentials were plotted as a function of distance from thedipole (spatial electrograms). Comparisons were made between specificelectrode configurations at maximum electrical potential (differencebetween maximum peak and trough). The ratio of the far field maximalamplitude to the near field maximal amplitude was calculated for OCU andbipolar configurations. The difference in maximal amplitude between OCUrecordings and bipolar recordings in parallel and perpendicularorientations relative to the DP.

To apply the electode model to moving charges, a cellular automatonmodel was used to create a two-dimensional plane of tissue (60×60cells). A standard action potential duration (action potentialduration=80) and resistance (R=13) was used. Two layers of evenly spacedelectrodes with standard electrode dimensions (1-mm length and 2-mmdiameter) were positioned in an array (10×10 electrodes) over the tissuesurface. The electrode array was used to record electrograms in bipolar,OCU, and unipolar orientations. The mean dominant frequency of therecorded electrograms from the different array types was compared withthe mean dominant frequency of the tissue directly underneath theelectrodes.

Electrogram recordings with standard catheters (2 mm electrode tip) weremade in 5 swine hearts. Recordings were made with a Bard recordingsystem. Catheters were held in place by a spacer that allowedsimultaneous recordings of CBP and OCU electrograms with a fixedinter-electrode spacing of 4 mm.

To assess near and far-field discrimination simultaneous CBP and OCUelectrograms were measured along the mitral annulus over the rightatrium. The CBP electrodes were oriented parallel to the annulus.

To assess the effect of wavefront direction, simultaneous CBP and OCUelectrograms were recorded over the right ventricle. Wavefront directionwas estimated by rotating the electrodes and spacer and finding therelative minimal amplitude of a CBP recording; simultaneous recordingswere made at that position.

Electrograms were analyzed offline. MATLAB®-based software was used tomeasure the amplitude of electrical signals. Groups of values werecompared with a Student's t-test.

In the in silico model there was a 0.72 mV difference in electricalpotential between CBP recordings in the parallel and perpendicularposition. Parallel to the direction of the wavefront, the recordedpotential was 1.88 mV. Perpendicular to the direction of the wavefront,the recorded potential was 1.15 mV. With the OCU configuration therecorded potential was 1.20 mV. The computer model used yields the sameabsolute values in multiple runs, and thus, does not define statisticalmeasures of variance with its use. FIG. 34 graphically illustrates nearfields spatial electrograms from a model, in accordance with embodimentsof the present invention.

In swine hearts there was an average 5.5+/−2.9 mV (mean±SD) differencein electrical potential between CBP recordings in the parallel andperpendicular position. Parallel to the direction of the wavefront, theaverage recorded potential was 9.1+/−3.1 mV. Perpendicular to thedirection of the wavefront, the average recorded potential was 3.6+/−0.7mV. With the OCU configuration the average recorded potential was4.0+/−0.7 mV, n=5.

In the in silico model average V/A ratio for the CBP configuration was0.09. In the in silico model average V/A ratio for the OCU configurationwas 0.05. FIG. 35 graphically illustrates far field spatial electrogramsfrom a model, in accordance with embodiments of the present invention.FIG. 36 illustrates graphically electrical potential recordings at asingle electrode, in a model, in accordance with embodiments of thepresent invention. FIG. 37 graphically illustrates membrane voltageunderneath a single electrode, in a model, in accordance withembodiments of the present invention;

There is a 55.5% reduction in the V/A ratio in the OCU configurationcompared to the CBP configuration. In swine hearts the average ratio ofventricular to atrial signal (V/A ratio) for CBP recordings along themitral annulus was 0.15+/−0.04, n=5. The average V/A ratio for OCUrecordings was 0.08+/−0.10. There is a 53.3% reduction in the V/A ratioin the OCU configuration compared to the CBP configuration.

In the FEM model with moving charges the average tissue DF was10.43+/−1.44 Hz. The average UNI electrode array recording DF was9.53+/−0.94 Hz. The average BP electrode array recording DF was10.84+/−1.45 Hz. The average OCU electrode array recording DF was10.33+/−1.36 Hz.

An electrode type (OCU) that ameliorates these limitations wasconceptualized with an understating of the physical limitations ofcurrent electrode designs. In a computer model with static charges, OCUis superior to CBP electrodes in resolving near and far field electricalactivity (55% decrease in the ratio of far and near-field signals), andOCU is independent of wavefront direction. In more clinical relevantconditions, multi-wavelet reentry was created in a cellular automaton.Here arrays of OCU electrodes demonstrated improved ability to identifytissue frequency than either unipolar or bipolar electrodes. Resultsfrom our animal study correlate with our results found in both of ourcomputer models.

OCU electrodes appeared to be superior in part because of the smallereffective electrode footprint compared with that of conventionalelectrodes. This may explain partially the improved tissue accuracy ofthe OCU electrode arrays. With complex moving wavefronts, the CBPelectrodes can be influenced by independent electrical events that canlead to erroneous estimates of the frequency of repetitive wavefrontswithin the tissue as a function of time.

OCU electrodes are superior compared with that of CBP electrodes withrespect to the ability to resolve near and far field activity. Geometryand relationship of the electrodes to the near and far field sourcesprovide for the improved electrodes. These results are consistent withthis in both the FEM model and our animal preparations.

The clinical implications of OCU electrodes are promising. For mappingcomplex arrhythmias and atrial fibrillation in particular arrays of OCUelectrodes with the spatial resolution and spatial sampling required tomore accurately discern tissue electrical activity may lead to moreeffective ablation procedures. A benefit of such arrays is that they canmaintain the OCU electrodes orthogonality relative to the tissuesurface, a key determinant of their effectiveness. OCU electrodes mayalso bear fruit in other fields that require sensors for electromagneticfields.

Thus, OCU electrogram recordings are superior to CBP recordings indifferentiating near field from far field activity (˜50% decrease in theratio of far and near-field signals) and retaining the wavefrontindependence of UP electrodes. Furthermore, OCU recordings are moreaccurate than those obtained with conventional electrodes in delineatingtissue frequency. It appears likely that deployed in arrays ofelectrodes, OCU electrodes will yield electrogam recordings that may beparticularly helpful in mapping complex arrhythmias and lead to moreeffective ablation procedures.

TABLE 1 Far/near field discrimination Directional dependence V/A ratioOrientation Orientation Parallel Perpendicular Difference Parallel OCUModel: CBP 1.88 mV 1.15 mV 0.72 mV (p = NA) Model 0.09 0.05 OCU 1.20 mVNA p = NA In CBP 9.1 ± 3.1 mV 3.6 ± 0.7 mV 5.5 ± 2.9 mV In vivo 0.15 ±0.04 0.08 ± 0.10 vivo: (p < 0.001) OCU 4.0 ± 0.7 mV NA p < 0.001 InTable 1: V = ventricular, A = atrial dimension; NA = not applicable;significance was defined as p ≤ 0.001.

In accordance with some embodiments of the present invention, one ormore electrodes are put in proximity to the cardiac tissue surface usingone or more catheters. Existing catheters and electrode configurationsused to assist in diagnosis and treatment of fibrillation have severalshortcomings for these purposes, including: (1) the inter-electrodespacing is too great; (2) the electrodes are too large; and (3) theelectrode configurations are not suitably orthogonal to the tissuesurface.

In a preferred embodiment, as diagrammed in FIGS. 38A and 38B, a pair ofelectrodes on catheter 801 are configured to be: (1) “orthogonal”; (2)“close”; and (3) “unipolar” (i.e., an “OCU” electrode configuration).

First, according to some embodiments, the inter-electrode axis fromindex electrode 382 to indifferent electrode 383 is “orthogonal” to thetissue surface 384. Existing catheters and electrode configurations arenot designed to be suitably orthogonal to the tissue surface. Eventhough existing catheters have been called “orthogonal” (e.g., the“Orthogonal Fixed” and “Orthogonal Deflectable” catheters available fromBiosense Webster® (Diamond Bar, Calif.)), a need has remained forcatheters with electrodes configured to be orthogonal (normal) to thesurface of tissue (i.e., in accordance with some embodiments of thepresent invention) as opposed to orthogonal to biological structures(e.g., fibers) on a surface for direction independent recordings. FIG.39 illustrates the difference between two curvilinear catheters incontact with tissue surface 391, where catheter 392 has a pair ofelectrodes with an inter-electrode axis orthogonal to the surface 391,and catheter 393 has a pair of electrodes with an inter-electrode axisthat is not orthogonal to the surface 391.

Second, according to some embodiments and as shown in FIGS. 38A and 38B,the inter-electrode distance 385 (i.e., the distance between the pair ofelectrodes) is “close.” For example, the inter-electrode distance 385may be within an order of magnitude of the electrode size (i.e., fromapproximately 0.1 mm to 3.0 mm). For example, the inter-electrodedistance 385 may vary from approximately 0.01 mm to 30.0 mm. Preferably,the inter-electrode distance 385 is between approximately 0.1 mm and 1mm so that the indifferent electrode is “close” enough to the tissuesurface to detect a signal. Thus, the proximity of the indifferentelectrode to the tissue surface may be determined by the thickness ofthe index electrode 382 and the inter-electrode distance 385.

Third, according to some embodiments, the electrode pair is “unipolar”because only the index electrode 382 may be in contact with the tissue.This unipolar electrode configuration has at least two advantages over acontact bipolar electrode configuration, in which both electrodes may bein contact with the tissue. The first advantage is that the unipolarelectrode configuration retains all of the spatial resolution benefitsof the contact bipolar configuration, but with the additional spatialresolution enhancement conferred by a smaller footprint (i.e., only halfof the electrodes may be in contact with the tissue surface). The secondadvantage is that the unipolar electrode configuration can retain theinter-electrode difference 385 independent from the direction of atissue activation wavefront. Contact bipolar electrogram amplitudedepends upon the direction of tissue activation. When an activationwavefront is parallel to the inter-electrode axis, the potentialdifference between bipolar electrodes is maximum, and the resultingelectrogram has maximum amplitude. However, when an activation wavefrontis perpendicular to the inter-electrode axis, the potential differencebetween bipolar electrodes is zero, and the resulting electrogram haszero amplitude. Furthermore, as the angle of incidence of a tissueactivation wavefront varies relative to the inter-electrode axis of acontact bipolar electrode configuration, fractionation may be producedin the resulting electrogram. Fractionation may also influence theelectrogram frequency, thus affecting accuracy in the assessment oftissue activation frequency. Therefore, the unipolar electrodeconfiguration can retain the inter-electrode difference 385 independentfrom the direction of a tissue activation wavefront and is immune tofractionation in response to changing wave-front direction.

FIG. 40 illustrates an example of improved spatial resolution obtainedby use of an OCU electrode configuration in accordance with someembodiments of the present invention. The tissue substrate surface 401is assessed by a catheter with one pair of recording electrodes in anOCU electrode configuration 402. The index electrode records electrogramsignal 403, and the indifferent electrode records electrogram signal404. The resulting OCU electrogram signal 405 is calculated bysubtracting the indifferent electrogram 404 from the index electrogram403.

In the example shown in FIG. 40, the tissue substrate surface 401contains three linear non-conducting scars (resulting, e.g., fromablation lesions). The scars separate the tissue surface 401 into fourconducting channels 406-409. The index electrode of the catheter is inclose proximity to and/or touching the tissue surface 401 directly abovethe second conducting channel 407. As indicated by the dashed arrows,the path of tissue activation within the vicinity of the recordingelectrodes is serpentine. The index electrode and indifferent electrodeelectrogram signals 403-404 exhibit large deflections at times 410-413as the tissue activation wavefront moves through the conducting channels406-409. However, the OCU electrogram signal x05 exhibits very smalldeflections at times 410 and 412-413 as the tissue activation wavefrontmoves through the conducting channels 406 and 408-409 not directlybeneath the catheter, and a much larger deflection at time 411 as thetissue activation wavefront moves through the local conducting channel407 directly beneath the catheter. Also, while each cell in the tissuesurface 401 was activated only once, the index electrode and indifferentelectrode electrograms 403-404 feature four deflections, indicating thata measurement of the frequency content of either electrogram would behigher than the true tissue activation frequency content of tissuesurface 401. Meanwhile, the frequency content of the OCU electrogram 405is a more likely indicator of the true tissue activation frequency.

Multi-Electrode Arrays

Atrial fibrillation is widely treated by catheter ablation, and iscurative in about 75% of patients. The remaining patients in whom atrialfibrillation persists would benefit from improved activation mappingmethods to resolve the complex dynamic patterns of tissue activationthat typify recalcitrant atrial fibrillation. Tissue activation patternsand their corresponding electric potential maps were simulated using acomputational model of cardiac electrophysiology, and sampled the mapsover a grid of locations to generate a mapping data set. Following cubicspline interpolation and an edge-extension and windowing method the datawas deconvolved and compared the results to the model current densityfields. Deconvolution can lead to improved resolution for arrays of10×10 electrodes or more that are placed within a few mm of the atrialsurface when the activation patterns include 3-4 features that span therecording area.

Atrial fibrillation is commonly treated with the use of catheterablation whereby lines of non-conducting tissue are created across theatria in an attempt to limit the patterns of electrical excitation toinclude only organized activity and not fibrillation. This procedure hasbeen found to have relatively high overall success rates, even thoughmultiple procedures are often required. In about 25% of cases, however,current approaches to catheter ablation fail to eliminate thisarrhythmia. These recalcitrant cases of atrial fibrillation generallyinvolve advanced disease of the atrial myocardium with extensive tissueremodeling. Knowing how to treat these difficult cases with theadministration of additional or alternative ablation lesions would beenormously facilitated by accurate mapping of the electrical activityover the atrial surface. Currently, clinical mapping entails the use ofa single roving electrode that is used to build up an isochronal map oftissue activation times relative to a fixed reference point.Unfortunately, this proves inadequate in atrial fibrillation because theactivation sequence involved is perpetually changing in random ways;sequential mapping yields ambiguous results in these situations. Thus,the only way to elucidate the atrial activation pattern in atrialfibrillation is to measure electrical activity simultaneously atmultiple locations.

An intra-cardiac electrode measures an electric potential that isgenerated by the combined electrical activities of each cell in theheart, the contribution from each cell being weighted in proportion tothe cell's current density and in inverse proportion to the lineardistance of the cell to the electrode. The recorded potential field isthus a blurred version of the tissue current density field, the latterbeing the desired reflection of tissue activation. This blurring processcan be approximated as a convolution of the current density field with apoint spread function that depends on the height of the electrode abovethe tissue.

A catheter design, such as illustrated in FIGS. 68, 69A-69B, and 70,that facilitates the arrangement of electrodes such that they arealigned normal to the tissue surface is described. In one possibleembodiment a soft flexible planar material is used. This is constructedsuch that while fully deployed (advanced out of a long sheath the end ofwhich is placed in the mapped chamber of the heart) the material isunfurled into a relatively flat surface 692, as shown in FIG. 69B. Thematerial is flexible enough that it can deform to the shape of the localtissue surface. Small, paired electrodes (see above) are placed directlyopposite each other on both sides of the surface. In this configurationwhen the catheter surface is in contact with the tissue these electrodepairs are orthogonal to the tissue. The end of the flat portion of thecatheter is smoothly tapered so that it can be pulled back into the longsheath and as it enters the sheath it furls to conform to thecylindrical shape 696 of the inside of the sheath.

The junction of the flat portion of the catheter (tip) with the cathetershaft is flexible enough that as the shaft is deflected forcing it toapproach a position in which the shaft is normal to the tissue surface,the flat portion bends relative to the shaft and is pushed into anorientation co-planar with the tissue surface.

In another embodiment, the catheter tip (flat portion) catheter shaftjunction acts like a hinge such that any pressure of the shaft towardsthe surface naturally places the tip into a co-planar orientationrelative to the tissue surface.

When mapping the heart's electrical activity one sometimes desiresmultisite-simultaneous information broadly distributed and at othertimes one desires more detailed information from a smaller region. It iscommon that these needs are sequential; first one makes a generalassessment of activation over a large area with low density of datapoints 680, based upon this data one identifies a sub-region (of thelarger recording area) in which a higher density of data 682, 694 isrequired. In one embodiment, a catheter design in which the flattwo-dimensional surface of the catheter tip is made from a distensiblematerial. Thus when distended the surface area is larger than when thesurface is not distended. Electrode pairs distributed as above (in pairson opposite sides of the tip surface) will be distributed over a smalleror larger area depending upon the amount of distension of the tipallowing for higher or lower density of recording sites. In either casethe distance between the electrodes on the bottom and top surface of thetip (the OCU pairs) remains fixed; as such this design allows for eachrecording site to have high (and unchanging) spatial resolution even asrecording site density is varied. Distention of the surface could beachieved with a loop of wire 702 (possibly constructed of nitinol) thatwhen advanced out of the catheter shaft increases the circumference ofthe tip surface. In another possible embodiment, as shown in FIG. 70,the tip can be constructed of an inflatable balloon, but with theballoon constructed such that it doesn't inflate in a spherical shaperather it inflates in a flat plate-like shape 704.

Variable recording site density can be achieved through the use of acatheter design in which electrodes on the two-dimensional array(described above) are not evenly distributed but rather are concentratedwith high density in one part of the catheter tip and lower density atother locations on the catheter tip. In this way using a single catheterand without need for changing the catheter size or shape one can focusdensity in one region while simultaneously having a broad view of otherareas. Much like the increased density of rods and cones in the Fovea ofthe retina.

Deconvolution

Numerical deconvolution of the measured potential field would thus seemto be a promising approach to extracting additional spatial informationabout patterns of tissue activation from multi-electrode recordings.However, even if such electrode arrays reach a high degree ofsophistication, the potential success of deconvolution for improving mapresolution is subject to a number of practical constraints. First, onlya finite number of electrodes can be placed simultaneously inside theheart, so the potential maps that they provide will inevitably becoarsely sampled versions of the desired continuous potential field. Ifthe sparseness is not too great, and a suitable interpolation scheme isused to approximate the missing data, then deconvolution may still leadto improved maps as has been shown previously. There is a secondconstraint, however, that is potentially more problematic. It is verylikely that high-density electrode arrays will be able to cover only amodest region of the atrial surface, thereby sampling a truncatedversion of the complete atrial activation pattern at any instant.Deconvolution of a truncated map leads to the phenomenon known asleakage, which can be ameliorated to a certain degree by eitherwindowing or by artificially extending the edges of the sampled map.

Understanding how sparseness and incompleteness affect the ability ofdeconvolution to reconstruct a tissue current density field from ofsampled potential field is important for optimizing the design of futureelectrode arrays. Accordingly, this was the goal of the present study.

Atrial tissue is considered to be two-dimensional, as would be the caseif one were mapping over a limited region and tissue thickness can beneglected. The electric potential, Φ, recorded by a point electrodelocated above the tissue consists of a contribution from the membranecurrent density in each cell in the tissue weighted inversely by itslinear distance to the electrode. Consequently, the transformationbetween the tissue membrane current density field and the potentialfield at height h can be described by the following integral equation:

$\begin{matrix}{{\Phi\left( {x,y,h} \right)} = {\frac{\rho_{e}}{4\pi}{\int_{- \infty}^{\infty}{\int_{- \infty}^{\infty}{\frac{I_{m}\left( {w,z} \right)}{\sqrt{\left( {x - w} \right)^{2} + \left( {y - z} \right)^{2} + h^{2}}}{dwdz}}}}}} & (13)\end{matrix}$where Im(x, y) is the membrane current density field, ρe is the specificresistivity of the medium between the tissue and the electrode (assumedto be blood), and w and z are dummy variables of integrationrepresenting the tissue spatial coordinates x and y. In other words,Φ(x, y, h) is the convolution of Im(x, y) with the point spread functionƒ(x,y,h)=[x ² +y ² +h ²]^(−1/2)  (14)

The problem addressed here is how to estimate Im(x, y) from anincomplete and coarsely sampled version of Φ(x, y, h).

Two-dimensional maps of Im(x, y) and Φ(x, y, h) were generated,representative of those likely to be encountered during atrialfibrillation using a computational model of cardiac excitation. Thismodel is a hybrid between a physics-based and a rule-based model isshown in FIG. 41A. Example of a truncated version of Φ(x, y, h) producedby the computational model of atrial excitation following sampling overa n×n grid and cubic spline interpolation between the samples. As shownin FIG. 41B, an extended version of the map in FIG. 41A with spatialderivative matching at the boundaries of the original grid. FIG. 41C isthe result of multiplying the map in FIG. 41B by the window describedherein. The map in FIG. 41C is denoted Φ(x, y, h) to be able torecapitulate the key dynamic features of the aberrant excitationencountered in atrial fibrillation, including meandering rotors andmulti-wavelet reentry. The model consists of a sheet of square cells,each of which represents a small patch of cardiac myocytes. These modelcells exhibit time-varying voltages according to the particularequations and rules that govern their behavior. The time-derivative ofthe voltage of a cell located at position (x, y) is taken to be Im(x,y), which then allows Φ(x, y, h) to be calculated according to Eq. 1.The dimensions of x, y and h are expressed in units of the edge lengthof a cell, which is nominally 1 mm.

The intra-atrial potentials are measured by a square array ofelectrodes. This is simulated by sampling Φ(x, y, h) at n×n equallyspaced grid points, and then use two-dimensional cubic splineinterpolation between the sampled points to create an estimate of thecomplete potential field over the region encompassed by the electrodearray. Varying the value of n thus allows us to experiment withdifferent spatial densities of electrodes. The electrodes themselves areassumed to have negligible extent. To simulate the effect of finitecoverage of an electrode array over the atrial tissue, the n×n samplesof Φ(x, y, h) are selected from a square subset of the simulated tissue.Then the edges of the data array are extended by adding syntheticsamples around the boundaries of the electrode positions in such a wayas to bring the spatially extended grid of sampled values smoothly downto zero. Simply adding extra data samples outside the original set doesnot guarantee, however, that the transition between the original dataand the extra samples will be smooth, something that is desirable whenperforming deconvolution in the Fourier domain in order to avoid theintroduction of spurious high frequencies in the deconvolved map.Therefore smoothness is ensured as follows. First the continuousfunction obtained by cubic spline interpolation of the original n×n datapoints are continued analytically past the boundaries of the grid to adistance of one quarter the nominal width of the point spread function.This width is defined as the horizontal distance from the peak of thepoint spread function to its value at 10% of peak. This extended Φ(x, y,h) is then multiplied by a window comprised of a central square sectionof unity height with a border consisting of a cosine bell so that itproceeds smoothly down to zero at its edges. The dimensions of thecentral section are the same as those of the original array of datasamples less one quarter of the nominal width of the point spreadfunction. FIGS. 41A-41C illustrate the edge extension and windowingprocess applied to an example Φ(x, y, h=2 mm) with n=20, yielding anapproximation to the true potential field that we denote Φ(x, y, h).

Deconvolution is performed in the spatial frequency domain by dividingthe fast Fourier transform of Φ(x, y, h) by the fast Fourier transformof f(x, y, h). To prevent amplification of noise arising from numericalerrors (and in real applications, also from measurement error), theoryof the Wiener filter is invoked by replacing simple division in theFourier domain by

$\begin{matrix}{{\hat{I}\left( {x,y} \right)} = {\mathcal{J}^{- 1}\left\{ \frac{\hat{\Phi}\left( {u,v,h} \right)}{{f\left( {u,v,h} \right)} + c} \right\}}} & (15)\end{matrix}$where I{circumflex over ( )}(x, y) is an estimate of I (x, y), ℑ⁻¹denotes the inverse Fourier transform of the bracketed quantity, andΦ(u,v,h) and f(u, v, h) are the Fourier transforms of Φ(x, y,h) and f(x,y, h), respectively. The constant c in Eq. 2 has the effect of adding asmall delta function to the point spread function. This serves toprevent division by something close to zero at those frequencies wherethe power in f(u, v, h) is zero, or very close to zero, and the power inΦ(x, y,h) is finite. In the present study, c=1 is set to suppress theeffects of noise without having a noticeable effect on the structures ofinterest in the deconvolved maps.

A current density field I(x, y, h) (left-hand panel) is measured at aheight of 2 mm as a blurred potential field Φ(x, y, h), as shown inFIGS. 42A and 42B. Deconvolution without any form of edge extension orwindowing yields a poor reconstruction of I(x, y, h) as shown in FIGS.42C and 42D. Deconvolution after edge extension and windowing asdescribed in the text yields a much better reconstruction. FIGS. 42A and42D illustrates the importance of edge extension and windowing whendeconvolving a truncated potential map. Without such edge processing,the deconvolved map contains high-frequency line artifacts that obscurethe details of the activation pattern (FIGS. 42A and 42B). When edgeprocessing is applied, these artifacts are effectively eliminated (FIGS.42C and 42D).

The goal in this study was to determine the conditions (i.e. the valuesof n and h) under which deconvolution provides a more useful picture oftissue activation than the raw samples of Φ(x, y, h) themselves. As anobjective measure of map accuracy, the mean squared residual (MSR) wascalculated between the actual current density distribution, Im(x, y),and the observed potential samples as

$\begin{matrix}{{MSR}_{obs} = \frac{\sum\limits_{i = 1}^{n^{2}}\left( {I_{i} - \Phi_{i}} \right)^{2}}{n^{2}}} & (16)\end{matrix}$where the index i is summed over all n2 electrode locations. Similarly,the MSR between Im(x, y) and the deconvolved map at the electrodelocations is

$\begin{matrix}{{MSR}_{dec} = \frac{\sum\limits_{i = 1}^{n}\left( {I_{i} - {\hat{I}}_{i}} \right)^{2}}{n^{2}}} & (17)\end{matrix}$

The relative benefits of performing deconvolution by this measure arethen indicated by the extent to which MSRobs is greater than MSRdec.

Nevertheless, much of the useful information in an activation mappertains to the details of the structural features present in the map,particular as it evolves dynamically in front of the observer, and theseare difficult to quantify. In fact, when any medical imaging modality isemployed to make clinical decisions, such decisions are usually made onthe basis of subtle pattern recognition processes that take place in themind of a trained observer. Accordingly, the value of deconvolution wasassessed through subjective evaluation of image sequences.

FIGS. 43A-43L demonstrates the ability of deconvolution to resolve asimple rotor, showing the true current density, the observed potentialfield, and the deconvolved estimate of the current density at two timesteps using arrays of FIGS. 43A-43F 20×20 electrodes and FIGS. 43G-43L10×10 electrodes. Deconvolution visibly improves the estimate of thecurrent density in both cases. These conclusions are borne out by thequantitative measures of accuracy shown in FIGS. 44A and 44B, whereI{circumflex over ( )}(x, y) can be seen to be improved over Φ(x, y,h)for electrode arrays greater than 3×3. Interestingly, the relativeimprovement in map accuracy is greater with the larger number ofelectrodes (FIGS. 43A-43F), showing that deconvolution becomesprogressively more worthwhile as electrode density over the tissueincreases. FIGS. 45A-45L illustrates a similar demonstration for a morecomplex activation pattern arising when a rotor begins to degenerateinto multi-wavelet reentry. Here, arrays of 30×30 and 15×15 electrodesare compared. In this case, the complex details in I(x, y) are almostimpossible to make out in □(x, y,h), but are for the most part readilyapparent in I{circumflex over ( )}(x, y), Again, the quantitativemeasures based on MSR (FIGS. 46A and 46B) bear out the visualimpressions arising from FIG. 5. That is, for most values of n, MSRdecis less than MSRobs. FIGS. 43A-43L. Maps of membrane current density(left), electrical potential (middle), and the deconvolved image (right)at two different time points in the evolution of a rotor obtained usingFIGS. 43A-43F a 20×20 array of electrodes at a height of 2 above thetissue. And FIGS. 43G-43L a 10×10 array of electrodes at the sameheight.

FIGS. 47A-47I illustrate the effect of increasing h upon both theobserved and deconvolved signals. Importantly, as h increases from 1 to5 the blurring in □(x, y,h) relative to I(x, y) becomes rapidly worse,and even the ability of our edgeprocessing technique to ameliorate thestreak artifacts in I{circumflex over ( )}(x, y) becomes severelydegraded (FIG. 47C). This demonstrates how important it is to place themapping electrodes as close to the cardiac tissue as possible. Even so,the deconvolved signal improves upon the raw data at heights up to 5.However, this is not always the case. FIGS. 48A-48B illustrates thatMSRobs becomes greater than MSRdec at a height of 10. Color videos ofthe progression of activation over time corresponding to FIGS. 43A-43L,45A-45L and 47A-47I are available on the web site repository. FIGS. 44Aand 44B. MSR for the observed and deconvolved signals relative to thetrue signal for the two activation patterns shown in FIGS. 43A-43L.Solid line—MSRobs, circles—MSRdec. The unit of MSR is the square of themodel cell dimension. FIGS. 45A-47L. True current density, observedsignal, and deconvolved signal using arrays of (a) 30×30 electrodes, and(b) 15×15 array electrodes, with h=2. The activation patternsrepresented here consist of two time points during the degeneration of arotor into multi-wavelet reentry.

Although catheter ablation therapy for the treatment of atrialfibrillation has an impressive success rate, effectively curing thecondition in about 75% of patients, it continues to present a majorclinical challenge in the remaining 25% in whom atrial fibrillationpersists [12]. These recalcitrant patients tend to have more advanceddisease characterized by complex patterns of atrial activity featuringintricate dynamic structures such as meandering rotors and multi-waveletreentry [13-15]. These patterns are often reflected in complexfractionated electrical activity seen on intra-cardiac electrograms,likely reflecting the simultaneous activity of a number of tissueregions that are close enough to the sensing electrode to contributesimultaneously to the recording [16]. Because of this complexity, andthe fact that these activation patterns typically change continually,elucidating the precise nature of tissue activation by sequentialmapping with a single roving electrode is not possible. Thus, electrodearrays in accordance with embodiments of the present invention that havethe spatial coverage and sampling density to resolve complex dynamicpatterns of tissue activation were developed. Prior art electrode arraysdo not have sufficient spatial resolution to fully resolve the mostcomplex activation patterns seen in cardiac fibrillation. Finer arraysof electrodes capable of measuring intra-cardiac potential at multipleclosely-spaced sites over a localized region of tissue will need to bedeveloped to facilitate atrial fibrillation mapping. Methods of digitalsignal processing can be used to enhance the spatial resolution of sucharrays beyond the physical limitations imposed by electrode size andnumber. FIGS. 46A and 46B illustrate the MSR for the observed anddeconvolved signals relative to the true signal for the two activationpatterns shown in FIGS. 45A-45L. The basic resolution enhancement issuein atrial fibrillation mapping can be expressed as a problem indeconvolution. Although straightforward in principle, in practicedeconvolution is fraught with a number of pitfalls related to noise anddata truncation. Fortunately, there are established methods for dealingwith these problems in general, although each deconvolution problemstands on its own merits in terms of the details of these methods. Inthe case of deconvolving maps of atrial fibrillation activity, the twomajor problems are sparseness of data sampling and incompleteness ofspatial coverage. The first of these is readily dealt with throughinterpolation between the measured data samples, the success of which isdependent upon the sampling density relative to the spatial frequenciesin the activation pattern being sampled. A previous study, for example,has applied this approach to the problem of distinguishing local fromdistant sources in electrogram recordings [8]. A potentially moreinsidious problem for deconvolution, however, arises when the sampledmap represents only a portion of the entire activation pattern, leadingto the problem of leakage contaminating the deconvolved image. There aretwo approaches to dealing with this problem, the most common being tomultiply the sampled data by a window that has a value of unity at itscenter while decaying smoothly to zero at the borders of the data array[5]. The problem with this approach, however, is that it eliminates asignificant amount of the data around the borders, which should beminimized given the sparseness of the original data set. The alternativeapproach is to extend the borders of the data array with synthetic datathat proceed smoothly to zero beyond the bounds of the original dataset. The disadvantage here is that the missing data must be guessed at.Therefore, a combined approach was intended to hedge against thedisadvantages of either method on its own. That is, the data wasextended beyond the boundaries of the original array of samples by onequarter of the width of the point spread function, and windowed theexisting data in from the boundary by the same distance. Furthermore,the extended data set was differentiable at the border between theoriginal and extended data points by matching the spatial derivatives attheir intersection (FIGS. 41A-41C). This led to a major improvement inour ability to recover the original tissue activation pattern bydeconvolution (FIGS. 42A-42D).

FIGS. 47A-47I illustrate the effects of electrode height on theresolution of a rotor, showing the true current density, the observedsignal, and the deconvolved signal at heights of FIG. 47A 1, FIG. 47B 3,and FIG. 47C 5. The deconvolution approach was applied to simulatedrotors (FIGS. 43A-43L and 47A-47I) and multi-wavelet reentry (FIGS.45A-45L), as these typify the kinds of complex activity patterns seen inatrial fibrillation. The results indicate that deconvolution can providea useful improvement in map resolution compared with raw electrode arrayrecordings. The accuracy of deconvolution is substantially improved byan edge processing technique that combines windowing and edge extension.Accuracy is also determined by the number of electrodes, electrodeheight, and tissue spatial frequency. The present study considered themapping electrodes to be of infinitesimal extent, whereas actualelectrodes have finite width and length. The finite dimensions of anelectrode cause it to measure a potential that is the average of thepotentials at each point on its surface, further contributing to theblur in a recorded map. In principle, deconvolution could attend to thisform of blurring as well, so the relative improvements seen withdeconvolution in the present study may not be as great as would beachievable with real electrodes. FIGS. 48A-48D. MSR for the observed anddeconvolved signals relative to the true signal for the activationpattern shown in FIGS. 47A-47I at heights of FIG. 47I 1, FIG. 47B 3, andFIG. 47C 5. Also shown are the MSR values for a height of 10 FIG. 47D.Solid line—MSRobs, circles—MSRdec. The electrode array characteristicsrequired for deconvolution to improve upon unprocessed potentialrecordings in human atrial fibrillation depend upon the tissue spatialfrequency of the atrial activity in such patients. Based upon highdensity mapping in humans with long standing persistent atrialfibrillation, it is likely that there can be greater than or equal to1.5 waves across each cm of atrium [15]. In this range of spatialfrequency deconvolution would improve spatial resolution for 10×10arrays in which inter-electrode spacing is ˜0.3 mm. Ultimately, ofcourse, this will need to be tested in humans with atrial fibrillation.In the meantime, the current modeling experiments allow us to accuratelycompare tissue current density distributions and electrogram recordings,something that is not possible in human experiments. These numericalexperiments inform us as to the kinds of electrode array characteristicsthat should be used when performing biologic confirmation.

The treatment of atrial fibrillation by catheter ablation is likely tobe accompanied in the future by attempts to map atrial excitation withelectrode arrays placed over tissue regions suspected of harboringcandidate ablation sites. The relationship between the recorded patternsof electric potential and the underlying tissue membrane current fieldscan be expressed as a convolution involving a point spread function thatdepends on the height of the electrode above the tissue[3]. Numericaldeconvolution thus has the potential to improve the spatial resolutionof recorded activation maps. A combination of interpolation between theelectrode recording sites and edge processing around the borders of theelectrode array ameliorates problems due to sparseness of sampling anddata truncation. Our results indicate that, when these issues areaddressed, deconvolution is likely to lead to improved resolution inrecorded potential maps when using electrode arrays of roughly 10×10 orgreater placed within a few mm of the atrial surface when attempting toresolve activation patterns with 2-3 features spanning the recordedarea.

In accordance with some embodiments of the present invention, theelectrogram frequency pattern may be measured simultaneously across atissue substrate to indicate the tissue activation frequency pattern,which indicates the circuit core density and distribution. For example,in certain embodiments, a multi-electrode array may be deployed viathoracotomy at the time of surgery, percutaneously, and/or transvenouslyand positioned over a region of cardiac tissue.

FIG. 49 illustrates a tissue substrate surface 491, over which atwo-dimensional multi-electrode array 492 has been deployed in OCUconfiguration in accordance with some embodiments of the presentinvention. In this example, 100 index electrodes 493 are paired with 100indifferent electrodes 494. Each pair of electrodes is itself in OCUconfiguration.

As described above, high spatial resolution at each recording site(e.g., each OCU electrode pair in a multi-electrode array) is importantfor electrogram signal frequencies to accurately reflect tissueactivation frequencies (and hence local circuit core densities). Themaximum distance between recording sites relates to the optimal distancebetween ablation lesions, which, in turn, relates to what extent thecircuit core density will be reduced in the area around a lesion as aresult of the lesion. Thus, even though high spatial resolution isimportant, the recording sites themselves need not be spaced extremelyclose together relative to the inter-electrode spacing in accordancewith some embodiments of the present invention. For example, themulti-electrode array in FIG. 49 may have an inter-electrode spacing ofonly 0.1 mm to 3.0 mm, but the distance between each OCU electrode pairmay be 5 mm to 10 mm).

FIG. 50 illustrates a tissue substrate surface 501, over which atwo-dimensional multi-electrode array 502 has been deployed inaccordance with some embodiments of the present invention. As in FIG.49, the array includes 100 OCU electrode pairs, each with one indexelectrode 503 and one indifferent electrode 504. However, unlike FIG.49, the multi-electrode array 502 itself is not orthogonal to the tissuesurface 501 (due to, e.g., incomplete apposition of the catheter withthe tissue). Unlike a catheter with a single pair of electrodes in OCUconfiguration, the orientation of a multi-electrode array may bedetermined without seeing the tissue. Examination of the electrogrammorphology may be sufficient to identify whether a multi-electrode arraytilted relative to the tissue surface 501. In FIG. 50, electrogramsignal 205 is more sudden with greater amplitude than electrogram 506,which is smaller and more gradual, thus indicating that the recordingposition for the electrogram signal 505 is closer to the tissue surface501 than the recording position for the electrogram signal 506. Thus, bycomparing the two electrograms 505-506, and without viewing the tissue(using, e.g., an imaging modality with a contrast agent), it can bededuced that the recording electrodes are not equally placed relative tothe tissue surface 501.

Each electrode in a multi-electrode array records a net electric fieldpotential, to which each cardiac cell contributes in an amountproportional to the cell's tissue current density and inverselyproportional to the linear distance from the cell to the electrode.Thus, the recorded net electric field potential may be a blurredapproximation of the tissue current density field, which is used toindicate tissue activation frequency and, in turn, the circuit coredensity and distribution.

In accordance with some embodiments of the present invention, thisblurring may be treated as though the tissue current density field wasconvolved with a spatially decaying point spread function, which can beestimated. Thus, numerical deconvolution of the measured net electricfield potential may be applied to extract information about the spatialnature of tissue activation frequency from multi-electrode recordingsand thereby improve spatial resolution.

The success of deconvolution for improving spatial resolution is subjectto a number of practical constraints in accordance with some embodimentsof the present invention. First, only a finite number of electrodes maybe simultaneously positioned inside the heart, so any resulting maps ofor based on net electric field potentials inevitably are sampledversions instead of continuous versions. If a sufficient number ofelectrodes are present, a useful continuous approximation to the truenet electric field potentials may be obtained by interpolating betweenthe samples according to some embodiments. A sufficient number ofelectrodes are present when the spatial frequency of the samplingapproaches the Nyquist criterion with respect to the spatial frequencycontent of the electric field potentials. Thus, in some embodiments, asuitable interpolation scheme (e.g., two-dimensional cubic splineinterpolation or another smooth interpolation function) may be used toapproximate the missing data in a map of or based on net electric fieldpotentials.

Second, the success of deconvolution for improving spatial resolution issubject to spatial truncation. In some embodiments, even a high-densitymulti-electrode array may cover only a modest region of the tissuesurface. Thus, only a spatially truncated version of the completepattern of net electric field potentials may be sampled at any instant.Deconvolution following spatial truncation leads to a phenomenon knownas “leakage,” which can be ameliorated by either windowing orartificially extending the edges of the sampled pattern of net electricfield potentials.

FIG. 51A is a process flowchart for improving spatial resolution usingdeconvolution in accordance with some embodiments of the presentinvention. In step 511, a spatially truncated intra-cardiac pattern ofnet electric field potentials is sampled using an m×n array ofelectrodes recording at height h above a tissue surface. In step 512,interpolation (e.g., two-dimensional cubic spline interpolation) isapplied to the m×n sampled data points to estimate a continuous functionrepresenting the complete pattern of net electric field potentials overthe region of tissue surface covered by the multi-electrode array. Instep 513, a point spread function is calculated from height h.

The truncated edges of the continuous function representing the completenet electric field potentials may be processed using a combination ofedge extension and windowing in accordance with some embodiments of thepresent invention. In step 514, the continuous function is analyticallyextended beyond the boundaries of the original m×n sampled data pointsto a distance of half the nominal width of the point spread function.The nominal width of the point spread function is the horizontaldistance from the peak of the function to the value at 10% of peak. Instep 515, the extended continuous function is multiplied by a window.The window may comprise, but is not limited to, a central rectangularsection of unity height. In accordance with some embodiments, thedimensions of the central section are the same as of the dimensions ofthe original m×n array of sampled data points less half the nominalwidth of the point spread function. FIG. 51B illustrates an exemplarywindow in accordance with some embodiments of the present invention.

In step 516, the continuous function and the point spread function aretransformed to the spatial frequency domain using, for example, the fastFourier Transform (“FFT”). In step 517, deconvolution is performed inthe spatial frequency domain by dividing the transformed continuousfunction by the transformed point spread function. In accordance withsome embodiments, a Wiener filter may be invoked and/or a small constantmay be added to the denominator when dividing in the spatial frequencydomain to prevent amplification of noise arising from numerical andmeasurement errors.

Patient-Specific Topological Maps for Tailored Treatment Strategies

As described above, a patient-specific map of a tissue substrateindicating appropriately acquired electrogram frequencies—which mayindicate tissue activation frequencies and, in turn, circuit coredensity and distribution—informs the optimal placement of ablationlesions to treat cardiac fibrillation.

FIG. 13 is a system component diagram in accordance with someembodiments of a system for detecting and/or mapping cardiacfibrillation in a patient. The system may include, but is not limitedto, a catheter subsystem 132, a processing unit 135, a memory 134, atransceiver 133 including one or more interfaces 139, a GUI 138, and/ora display 136 (each described in detail below). The system may alsoinclude, but is not limited to, an ECG/EKG subsystem 130 and/or animaging subsystem 131 (described above).

The catheter subsystem 132 may be configured for determiningpatient-specific (and location-specific) tissue spatiotemporalvariations, mapping one or more measurements indicative of the densityand distribution of circuit cores, and/or assessing the efficacy of atreatment procedure (e.g., whether ablation lesions completely preventconduction in both directions).

A catheter in the catheter subsystem 132 may be configured to performone or more types of procedures according to some embodiments of thepresent invention. In a preferred embodiment, a catheter for mapping oneor more measurements indicative of the density and distribution ofcircuit cores (i.e., a “mapping catheter”) includes one or more pairs ofrecording electrodes in the OCU electrode configuration. In someembodiments, a mapping catheter includes a two-dimensional array ofrecording electrodes, in which the electrodes are preferably: (1) assmall as possible (without incurring too great an increase in noise thatresults from high impedance); (2) of sufficient number so thatdeconvolution confers a spatial resolution advantage; and (3) orientedwith an inter-electrode relationship that facilitates improved spatialresolution (i.e., the OCU configuration).

According to some embodiments of the present invention, the same or asimilarly configured catheter in the catheter subsystem 132 may be usedfor identifying the optimal spatial resolution for local tissue withspatiotetmporal variation. For example, FIGS. 52A and 52B illustrate asimilarly configured catheter with more than two electrodes on an axisorthogonal to the tissue surface.

According to some embodiments of the present invention, the same or asimilarly configured catheter in the catheter subsystem 132 may be usedfor mapping and/or assessing the efficacy of a treatment procedure. Forexample, a similarly configured catheter also may be used to assesswhether an ablation lesion completely prevents conduction by selectingone electrode on either side of the lesion for pacing, and thenrecording the tissue activation timing on the remaining electrodes toquickly identify the presence or absence of a complete conduction block.By selecting one electrode on the opposite side of the lesion forpacing, a complete bi-directional conduction block may or may not beconfirmed. (by pacing from both sides of the ablation lesion one canconfirm bi-directional block).

According to some embodiments of the present invention, a similarlyconfigured catheter in the catheter subsystem 132 may be used fortreating cardiac fibrillation. In some embodiments, a similarlyconfigured catheter also may include an ablation electrode configuredfor creating point and/or linear ablation lesions in the heart tissue.FIGS. 53 and 54 illustrate different views of a catheter configured forboth mapping, minimizing, and treating cardiac fibrillation. Forexample, an ablation electrode may be included on one of a multiple ofcatheter splines while one or more pairs of recording electrodes may beincluded on a separate catheter spline. Or, an ablation electrode may beincluded as part of a multi-electrode array, such that mapping, lesionassessment, and ablation treatment may all be performed using a singlecatheter. According to some embodiments of the present invention, thesystem for detecting and mapping fibrillation may also include one ormore processing units, shown collectively in FIG. 13 as processing unit135, that process instructions and run software that may be stored inmemory. For example, processing unit 135 executes applications, whichmay include, but are not limited to, catheter-related applications forpositioning electrodes and recording electrograms; signal processingapplications for performing, for example, deconvolution processes; andtopological mapping applications for identifying reentrant circuit coredensity and distribution in the heart. In some embodiments, the softwareneeded for implementing a process or a database includes a high levelprocedural or an object-orientated language such as C, C++, C#, Java,Perl, or MATLAB®. The software may also be implemented in assemblylanguage if desired. Processing unit 135 can be any applicableprocessing unit that combines a CPU, an application processing unit, andmemory. Applicable processing units may include any microprocessor(single or multiple core), system on chip (SoC), microcontroller,digital signal processor (DSP), graphics processing unit (GPU), combinedhardware and software logic, or any other integrated circuit capable ofprocessing instructions.

According to some embodiments of the present invention, the system fordetecting and mapping fibrillation may also include one or more memorydevices, shown collectively in FIG. 13 as memory 134. Memory 134 storesthe instructions for the above applications, which are executed byprocessing unit 135. Memory 134 also may store data relating todetecting and mapping fibrillation, such as the electrogram recordingsand frequencies.

According to some embodiments of the present invention, the system fordetecting and mapping fibrillation may also include one or moretransceivers, shown collectively in FIG. 13 as transceiver 133.Transceiver 133 includes a transmitter and a receiver. The transmitterand the receiver may be integrated into a single chip or may be embodiedin separate chips, or may be integrated with processing unit 135 and/ormemory 134. Transceiver 133 may also include one or more interfaces 139,that provide an input and/or output mechanism to communicate with otherdevices, such as the catheter subsystem 132. As an input and/or outputmechanism, interface(s) 139 may operate to receive electrogramrecordings from as well as transmit instructions to the cathetersubsystem 132. Interface(s) 139 can be implemented in software orhardware to send and receive signals in a variety of mediums, such asoptical, copper, and wireless, and in a number of different protocolssome of which may be non-transient.

According to some embodiments of the present invention, the system fordetecting and mapping fibrillation may also include a GUI 138 to providecommunication with an input and/or output mechanism to communicate witha user. For example, a clinician may use input/output devices tosend/receive data to/from the processing unit 135 and catheter-basedsubsystem 132 over the GUI 508. Input devices may include, but are notlimited to, a keyboard, a touch screen, a microphone, a pen device, atrackball, a touch pad, and a mouse. Meanwhile, output devices mayinclude, but are not limited to, a display 136, a speaker, and aprinter. Other input/output devices may also include, but are notlimited to, a modem and interface(s) 139 of transceiver 133. The GUI 138can operate under a number of different protocols, and the GUI interface138 can be implemented in hardware to send and receive signals viatransceiver 133 in a variety of mediums, such as optical, copper, andwireless.

FIG. 55 is a process flowchart for detecting and mapping fibrillation inaccordance with some embodiments of the present invention. In step 551,a puncture is made in a distal vessel, a guidewire is inserted, and avascular sheath is threaded over the wire. A mapping catheter with amulti-electrode array is inserted using a guidewire and moved toward theheart. Alternatively, this insertion can be made percutaneously via thechest or via thoracotomy at the time of surgery. In step 552, thecatheter is positioned so that the one or more inter-electrode axes areorthogonal to the surface of the tissue substrate. Once the mappingcatheter is in position, an OCU-configured electrode pair or array maybe engaged in one tissue location or region at a time so that an arrayof signals (e.g., net electric field potentials) may be recorded in step553. In optional (but preferred) step 554, the signal recorded by eachorthogonal indifferent electrode is subtracted from the signal recordedby its associated index electrode to acquire a new array of signals. Instep 555, signal processing including, but not limited to,interpolation, edge extension and windowing, FFT, deconvolution, and/orcalculation of the centroid of a signal power spectrum is performed toreturn values (e.g., local electrogram signal frequencies as defined bythe centroid of the power spectrums) indicative of tissue activationfrequencies, which are indicative of reentrant circuit core density anddistribution across the tissue substrate.

In step 556, these values are mapped (e.g., in a color-coded fashion)onto a representation (e.g., a two-dimensional image orthree-dimensional model) of the tissue substrate surface according tothe positions of the recording electrodes, which are identified using anappropriate electrode localization technology.

FIGS. 56A-56C illustrates the relationship between: (FIG. 56A) an OCUelectrogram frequency map of a tissue substrate indicating circuit coredensity and distribution (using the centroids of the power spectrums);(FIG. 56B) an OCU electrogram recording for a location 1801 in themapped tissue substrate; and (FIG. 56C) the power spectrum derivedthrough FFT of the OCU electrogram in accordance with some embodimentsof the present invention. At location 561 in the tissue substrate shownin FIG. 56A), electrogram signals of an index electrode and itsassociated indifferent electrode, which are in OCU configuration andlocated above location 561 in the tissue substrate, are recorded. Theresulting OCU electrogram (i.e., the difference between the two signals)for location 561 is shown in FIG. 56B. The local electrogram frequencyat location 561 is calculated by deriving the power spectrum of the FFTof the OCU electrogram. FIG. 56C is a plot of the power spectrum, onwhich centroid 562 has been calculated and marked. The value of thecentroid 562 of the power spectrum is mapped onto a representation ofthe tissue substrate at the coordinates for location 561 to indicatetissue activation frequency, which is indicative of circuit coredensity, at location 561.

FIG. 57 is a map of a tissue substrate indicating tissue activationfrequencies, which are indicative of circuit core densities, inaccordance with some embodiments of the present invention. In thisexample, the values on the map are the local electrogram signalfrequencies as defined by the centroid of the respective powerspectrums. FIG. 57 illustrates the impact of selecting a thresholdfrequency to define the size and number of high circuit core densityregions across a tissue substrate in accordance with some embodiments ofthe present invention. For example, if threshold frequency 571 isselected for this tissue, four regions of high circuit core density,including region 573 and region 574, are indicated. However, if a lowerthreshold frequency 572 is selected, all of the regions expand andregion 573 and region 574 are fused into one high circuit core densityregion 575.

Optimization of Lesion Distribution

The efficiency of ablation lesions can be maximized by making use of thepreviously identified locations of high circuit core density. Becausehigh circuit density sites can be distributed throughout the surface ofthe atrial tissue in complex arrangements that vary by patient, findinga distribution of ablations that overlaps the largest number of highcircuit density sites and connects to the tissue edge with the smallesttotal lesion length is an important optimization question.

The connection of multiple sites using the shortest possible distance isas a combinatorial optimization problem that can be solved using anumber of computer-based algorithmic solutions. For a small number ofsites, the problem can be solved by exact algorithms, comparing everypossible permutation to find the optimal solution. The complexity of theproblem rises at the rate of O(n!). Thus, as the number of sites nincreases, solving the problem by exact algorithms become increasinglyinefficient and impractical.

Instead, heuristics or approximation algorithms can be used to reach asolution very quickly for large numbers of sites, although the solutionmay not be optimal and complete. Heuristics algorithms iterativelyimprove a solution until search termination criteria are met, ratherthan exploring every permutation. Different algorithms have differentmethods for choosing permutations on their iterations. The terminationcriteria can include the number of iterations, a threshold value, thespeed at which a solution is improving, or a number of iterationswithout improvement. Some examples of heuristics algorithms includegreedy algorithm, genetic algorithm, simulated annealing, particle swarmoptimization, and ant colony optimization.

In some embodiments, a genetic program, which is a specialization ofgenetic algorithms, is used to solve this optimization problem. Thegenetic program iteratively improves a solution based upon theprinciples of evolution and “survival of the fittest.” In certainembodiments, “fitness” is characterized as a line distribution thatcovers the largest total circuit density with the smallest number ofablation points (i.e., shortest total lesion length). The program mayalso incorporate constraints such as, for example, avoidance of ablatingacross atrial arteries. Additional fitness criteria can be added so thatthe search strategy reflects current best lesion distributioncharacteristics. Embodiments of cardiac fibrillation detection andmapping system may use the genetic program to identify and, optionally,display the highest efficiency distribution of lesions to connect the“peaks” in the topological map representing circuit core density anddistribution. This information can then be used by a clinician basedupon complete consideration of the clinical context.

As shown in FIG. 58, the genetic program provides a hierarchicaltree-like structure to define the genotype of its solutions inaccordance with some embodiments of the present invention. Embodimentsof the genetic program take a unique approach in which the genotype isalso the phenotype. In other words, the tree-like structure itselfrepresents the distribution of ablation lesions. The individual elementsare potential sets of ablation lesions (i.e., an ablation lesion set).Thus, an individual element is defined by the locations of itsconnection(s) to the tissue's boundary edge, the first branch point,subsequent branch points and each end point. The fitness of eachindividual element in a population is measured as the total density ofthe map points that that ablation lesion set overlaps.

In a series of experiments using a computational model, tissue (80×80cells) was created with heterogeneous electrophysiologic properties.Specifically, the tissue had two different regions, each region havingvariability of action potential duration randomly distributed around amean value. In the majority of the tissue, the action potential durationmean was 130 ms (with an intercellular resistance of 9 ohms). However,in one square patch of the tissue (26×26 cells), the action potentialduration mean was 80 ms (with an intercellular resistance of 13 ohms).

Burst pacing (from each of 64 pacing sites) was applied during multiplesimulations in each tissue region. In the presence and absence ofablation lines extending from a tissue edge, measurements were obtainedof (1) the percentage of instances in which pacing resulted insuccessful induction of multi-wavelet reentry, and (2) the duration ofeach episode of multi-wavelet reentry. The location, length, and numberof ablation lines were randomized over 500 iterations.

The total ablation line lengths (aggregated from the lengths ofindividual ablation lines in each set) were calculated and varied from 0to 150 cells. Measurements of the average circuit density of the cellsat each ablation site were obtained and used to calculate the averagecircuit density underneath the entire ablation line set. Of the total500 ablation line sets, 10 sets were selected based upon their averagecircuit density overlap such that there was an even distribution ofablation line sets ranging from minimal to maximal circuit densityoverlap.

Also calculated, as a function of total ablation length and circuitdensity overlap, were (1) the time to termination of induced episodes ofmulti-wavelet reentry, and (2) the percentage of attempted inductions(pacing episodes) that successfully produced sustained multi-waveletreentry. FIGS. 64-65 are two views of a three-dimensional plot of thetime to termination of induced episodes of multi-wavelet reentry(z-axis) as a function of total ablation length (x-axis) and circuitdensity overlap (y-axis) in accordance with some aspects of the presentinvention. FIGS. 64-65 reveal that time to termination is reduced as (1)total ablation length increases and (2) circuit density overlapincreases. FIGS. 64-65 also reveal that the relationship between time totermination and total ablation length is largely linear when circuitdensity overlap is low but distinctly non-linear when circuit densityoverlap is high. With high circuit density overlap (compared to lowcircuit density overlap), there is a marked reduction in time totermination with a smaller total ablation length. Thus, when ablationlesions are placed so as to maximize circuit density overlap, greaterefficiency may be achieved (i.e., greater reduction in time totermination per amount of ablation). Also, the total ablation lengthreaches a point of diminishing returns in terms of the impact on time totermination. that time to termination begins to decline steeply when anablation line extends from a tissue edge to the high circuit densitypatch and that the point of diminishing returns is reached when theablation line extends through the high density patch.

In another series of experiments using a computational model, thedistance of the high circuit density patch from the edge of the tissuewas varied, as was the size of the patch. FIGS. 66-67 are two views of athree-dimensional plot of the percent inducibility (z-axis) as afunction of total ablation length (x-axis) and circuit density overlap(y-axis) in accordance with some aspects of the present invention. FIGS.66-67 reveal that (1) at low circuit density overlap, inducibility ofmulti-wavelet reentry steadily increases as total ablation length isincreased, and (2) at high circuit density overlap, the relationshipbetween total ablation length and inducibility is non-linear (e.g.,increasing total ablation length first increases, then markedlydecreases, and finally again increases inducibility).

Additional experiments demonstrated that (1) ablation lines delivered tosites of low circuit density increase inducibility, and (2) ablationlines delivered to sites of high circuit density decrease inducibility.Inducibility began to decrease once ablation lines reached the highcircuit density patch and continued to decrease until the ablation lineextended through the patch (the “to and through” approach). Once theablation line extended beyond the high circuit density patch into thelow circuit density regions, inducibility began to rise again.

Together, the experimental data data indicate that accurate circuitdensity maps allow for determination of the ideal total length andplacement of ablation lesions so as to maximize the efficiency ofablation at reducing time to termination and the efficacy of ablation atminimizing inducibility of multi-wavelet reentry.

FIG. 13 is a system component diagram in accordance with someembodiments of a system for optimizing the placement of ablation lesionsin a patient's heart. The system may include, but is not limited to, aprocessing unit 135, a memory 134, a transceiver 133 including one ormore interfaces 139, a GUI 138, and/or a display 136 (each describedabove).

FIG. 59 is a process flowchart for applying a genetic algorithm foroptimizing lesion placement to a map indicating circuit core density anddistribution according to some embodiments of the present invention. Instep 591, one or more measurements indicating reentrant circuit coredensity and distribution across a tissue substrate are mapped. In step592, a threshold (e.g., the top 20%) is selected to identify highcircuit core density regions. In step 593, the high circuit core densityregions are circumscribed. In step 594, a random initial ablation lesionset (i.e., a sample) is generated. The random sample may include apopulation of, for example, 100 potential lesions. Each potential lesionin the sample connects a high circuit core density region with a tissueboundary. The connection between a high circuit core density region anda tissue boundary may be direct or indirect. That is, a lesion line maybe connected to another lesion line and/or a tissue boundary. Theconnection between high circuit core density regions and between a highcircuit core density region and a tissue boundary may be linear,curvilinear, or some other shape, as long as the connections arecontinuous. In step 595, total length of the proposed ablation lesionsis optimized, which can be used for the fitness selection in step 596.During the fitness selection, elements with the highest fitness arechosen. For example, two elements in the sample could be chosen. Thenumber of elements to be selected is based on an optimization parameter.The chosen elements based on the fitness selection are used to producethe next generation in step 599, while the other individual elements arediscarded. In step 597, the computer algorithm decides if terminationcriteria is met. If the termination criteria is met, the optimization iscomplete as shown in step 598. Otherwise, in step 599, a new generationof individual elements is created through mutation and crossover fromthe “parents.” Mutation changes one or more elements of the solution butleaves other elements, thus creating a slight variation. Crossoverderives a new solution based on parts of two or more parents. Forexample, a first half of the solution comes from one parent and a secondhalf comes from another parent. Then the process returns to step 592:fitness calculation. The fitness of each individual element in this newgeneration is calculated so that the fittest may be chosen. The processis repeated and the fitness of the solution evolves to maximize thetotal density of the map points covered while minimizing the extent ofablation.

However, as a solution evolves, its effectiveness does not improvelinearly with its efficiency. There is a point of diminishing return forablation lesion concentration within the high circuit density region.After this point it is advantageous to distribute any additional lesionsin the remaining tissue based on an ideal inter-ablation-line distance.

Assessment of Fibrillogenicity

FIG. 13 is a system component diagram in accordance with someembodiments of a system for assessing fibrillogenicity in a patient. Thesystem may include a catheter subsystem 132, a processing unit 135, amemory 134, a transceiver 133 including one or more interfaces 139, aGUI 138, and/or a display 136 (each described above). The system mayalso include, but is not limited to, an ECG/EKG subsystem 130 and/or animaging subsystem 131 (also described above).

FIG. 60 is a process flowchart for quantifying and/or assessingfibrillogenicity in a patient in accordance with some embodiments of thepresent invention. In step 601, initial fibrillogenicity is assessed. Instep 602, electrograms are acquired, from which electrogram frequenciesare derived in step 603. In step 604, the frequencies indicative ofcircuit density and distribution are mapped. The process then includesstep 605, in which ablation lesion placement is optimized. In step 606,fibrillogenicity is quantified and compared with a predeterminedthreshold. In step 607, ablation lesion therapy is applied, and theprocess iterates back to step 602, wherein new electrograms areacquired. The process is completed in 608, once the measure offibrillogencity meets is below the predetermined threshold.

Feedback-Driven Ablation Treatment

After introducing an ablation lesion, clinicians may determine ifadditional lesions should be placed. This determination can be made bymeasuring the tissue activation frequency following an ablation. If thetissue activation frequency becomes lower than a threshold frequency,then the process of ablation treatment ends. However, if the tissueactivation frequency is higher than a predetermined threshold frequency,clinicians may add more lesions.

FIG. 13 is a system component diagram in accordance with someembodiments of a system for iteratively treating cardiac fibrillation ina patient. The system may include a catheter subsystem 132, a processingunit 135, a memory 134, a transceiver 133 including one or moreinterfaces 139, a GUI 138, and/or a display 136 (each described above).The system may also include, but is not limited to, an ECG/EKG subsystem130 and/or an imaging subsystem 131 (also described above). FIG. 62 is asystem diagram, in accordance with embodiments of the present invention.FIG. 62 describes the EKG subsystem 621, imaging subsytem 622, andcatheter subsystem 623, as detailed above.

FIG. 61 is a process flowchart for treating cardiac fibrillation in apatient using iterative feedback in accordance with some embodiments ofthe present invention. In step 611, one or more measurements indicativeof circuit core density and distribution are mapped. After finding theregions with higher circuit density from the map, an optimization methodis applied to find the optimal distribution of ablation lesions in step612. The optimization may be based on the regions with, for example, thetop 30% of the highest circuit core density sites. In step 613, theatria of a patient are ablated based on this optimal distribution. Instep 614, clinicians use a catheter, preferably a mapping catheter inaccordance with the systems of the present invention, to ascertain thepresence or absence of bidirectional block across ablation lesions. Instep 615, a determination is made as to whether the ablation lesions areor are not complete as performed (i.e. is further ablation required toachieve bidirectional block?). If bidirectional block is not complete,the process goes back to step 613 and additional ablation is added. Ifbidirectional block is complete, then F-wave cycle length is checked instep 616. In step 617, a determination is made as to whether the F-wavecycle length is greater than, for example, 180 milliseconds. If theF-wave cycle length is greater than 180 milliseconds, ablation therapyis complete. Otherwise, if the F-wave cycle length is less than 180milliseconds, the entire process repeats beginning at step 611.

Ablation lesions may be produced via tissue heating or cooling. Suchenergies include radiofrequency, high frequency and/or focusedultrasound, laser, microwave or cryo-technologies. The only requirementis that tissue be irreversibly damaged such that recovery of conductioncannot occur.

As will be apparent to one of ordinary skill in the art from a readingof this disclosure, the present disclosure can be embodied in formsother than those specifically disclosed above. The particularembodiments described above are, therefore, to be considered asillustrative and not restrictive. Those skilled in the art willrecognize, or be able to ascertain, using no more than routineexperimentation, numerous equivalents to the specific embodimentsdescribed herein. The scope of the present invention is as set forth inthe appended claims and equivalents thereof, rather than being limitedto the examples contained in the foregoing description.

The invention claimed is:
 1. A catheter-based system optimized formapping cardiac fibrillation in a patient, the catheter-based systemcomprising: a catheter comprising an array of a plurality of stackedelectrode pairs, each electrode pair including a first electrode and asecond electrode arranged in an orthogonal, close, unipolar (“OCU”)electrode configuration, wherein each electrode pair is configured to beorthogonal to a surface of a cardiac tissue substrate, wherein eachfirst electrode is configured to be in contact with the surface torecord a first signal, and wherein each second electrode is separatedfrom the first electrode by a distance which enables the secondelectrode to record a second signal, and a processor configured toreceive and process one or more measurements obtained from at least afirst signal and a second signal recorded by at least a correspondingone of the stacked electrode pairs in response to electrical activity inthe cardiac tissue substrate indicative of a number of electricalcircuit cores and distribution of the electrical circuit cores for aduration across the cardiac tissue substrate in the patient's heart. 2.A catheter optimized for assessing efficacy of an ablation procedure ina patient, the catheter comprising: an array of a plurality of stackedelectrode pairs, each electrode pair including a first electrode and asecond electrode arranged in an orthogonal, close, unipolar (“OCU”)electrode configuration, wherein each electrode pair is configured to beorthogonal to a surface of a cardiac tissue substrate, wherein eachfirst electrode is configured to be in contact with the surface torecord a first signal, and wherein each second electrode is separatedfrom the first electrode by a distance which enables the secondelectrode to record a second signal, wherein the catheter is configuredto obtain one or more measurements from at least a first signal and asecond signal recorded by at least a corresponding one of the stackedelectrode pairs in response to electrical activity in the cardiac tissuesubstrate indicative of a number of electrical circuit cores anddistribution of the electrical circuit cores for a duration across thecardiac tissue substrate in the patient's heart.